Avoiding "enlightenment" experiences while meditating for anxiety?

In general I think this is not possible. That's because the thing we call awakening or enlightenment is just noticing the world as it as and responding our experience of the world to include it rather than close it out. It's not something special, just the mundane realization of life as it is. That we build it up into something is because we have trouble making sense of it when we've not fully experienced it.

To me your question is a bit like asking how can I have my eyes open and avoid seeing any colors when you believe the world is black and white. Trouble is, you're already seeing the colors, even if you're really good at ignoring them. Anything you do might cause you start noticing them, and an activity designed to help you notice things will only be especially good at this.

If you're really set on this goal, though, there are ways you could try to actively avoid noticing the world. Don't do meditation like described in TMI or any Buddhist text. In fact, don't meditate at all. Also stay away from psychedelics. Instead, you can learn to hypnotize yourself to put yourself into trance states. This is a bit like the stupor benzos and alcohol induce. I don't recommend it, and it can be habit forming, but it exists as an alternative to facing reality as it already is.

I think more concentration meditation would be the way, but concentration meditation does lead to more likely noticing experiences that cause what you may call “awakening experiences”. (This is contrast with insight meditation like noting)

Leigh Brasington’s Right Concentration is a book on jhana’s, which is becoming very concentrated and then focusing on positive sensations until you hit a flow state. This is definitely not an awakening experience, but feels great (though I’ve only entered the first a small amount).

A different source is Rob Burbea’s jhana retreat audio recordings on dharmaseed.

This is a difficult line to thread, since while I can't be sure which awakening experiences you're opposed to in particular (incidentally, see the later paragraphs re: variations between them), as a general category they seem to be the consequence of your intuitive world-model losing a mysterious "self" node to be replaced with a more gears-like representation of internal mental states and their mechanisms.

However, you might be able to make it more difficult to "look" in that direction by using vipassana-style meditations with limited time. This should lead you to disproportionately 'collapse' your anxiety and other imprinted/background thought patterns and intrusive thoughts, which would start out clamoring for your attention, and not make much progress noticing the more fundamental phenomenological nature of experience itself. You'd also have to keep in mind an intention to not apply your mindfulness to the roots of your experiential state after the meditation period itself, since (in my experience at least) you continue to perceive your experiences meditatively for a while after meditation.

I am curious, however, what specifically you are avoiding from awakening experiences? 

I'll acknowledge (as someone who hasn't yet experienced it myself) that "enlightenment" seems to be more a descriptor/category than a singular state, and as such there are ways to reach it which might not be the best by your preferences. Personally I'm trying to avoid preference-dissolution (I haven't actually found any traditions which lead in that direction, but it's a concern of mine regardless) or the methods which rely heavily on more-traditionalist interpretations of "Right View" to stabilize your normal mind through the dissolution of the assumption of self (which, being millennia-old and somewhat dependent on mostly-blind faith, tend to contradict my strong preference for non-supernatural, fundamentally-gears-like world-models).

But I'm finding it hard to think of a reason to be opposed to all the paths to awakening, especially since there exist some monks who explicitly claim no changes in surface-level mental structure from their enlightenment experiences (Enlightenments is an interesting article mentioning this, found in this [LW(p) · GW(p)] LW comment), so it would be interesting to know the one driving you. Or is there some particular way The Mind Illuminated defines awakening which is problematic for you?

I wonder if you might have it backwards: Building concentration up to TMI level 4/5 may have been enough to push your sensory system far enough into insight territory that the anxiety and panic that you are experiencing now may, in fact, be symptoms of a Dark Night (or partly so). In that case, the "standard" prescription is *more* insight practice, not less.

If you would like to look into that line of reasoning, Daniel Ingram's (highly opinionated but very valuable) book would be a standard source to learn more about Dark Nights. Also you could check out Cheetah House's website to see if you can relate to their description of symptoms.

In any case I'd second Logan Riggs recommendations. The recordings of Rob Burbea's jhana retreat are amazing.

You might focus on brahmavihara meditations that don't need to involve deeply concentrating the mind. These tend to be more about cultivating deep habits of thinking kind thoughts while holding a target in mind. Enough of this helps to make it more likely that those kinds of thoughts might come up automatically (especially in more stressful situations).

In case you're unfamiliar, the basic instructions look like this (with most of the jargon stripped away for the group's reading pleasure): One at a time, for each person in {someone you're close with, yourself, someone you're not close with, someone you have a hard time with}, hold the target in mind and think "Be happy. Be healthy. Be safe." (or whatever equivalent phrases make sense to you) at a pace that lets you connect with each thought. No need to feel a certain way about it, just think about what each thought means and notice if any feelings do come up. Repeat for a few minutes for each person, or until you get where you're going if that's your inclination.

My understanding is that seeing the metaphorical matrix is something you (usually) have to work at on purpose, so I'd guess you simply don't have to go any further than you want to on that front. Holding back on both concentration practices (which may produce altered states) and insight practices could be the ticket, but I should think it likely likely to make brahmavihara practices a bit harder if you don't have at least some of the other two.

All that said, most of the mood benefits I've gained from my own practice have been a result of getting a better handle on reality, so you may find that you're working at cross purposes with yourself on this one. And as with all things, remember to review your preferences, systems, and habits from time to time and see if everything's working together the way you want it to.

Stay safe. :)