Oh, I actually skipped over that question, sry bout that. I just put in my range vs my range to show how huge the range asymmetry is. But the problem is, that PS default ranges are not really useful.
It's pretty hard to work with "PS default" ranges, cause they're built up in a fashion that totally disregards balance, mostly focusing on hot-cold equity, and also less applicable in today's games (nits are not as common these days sadly). Working with those ranges actually makes 88 a clear bluff (it's in the bottom 18% of our overall range on this board) - you can see, why these preflop ranges don't make sense in a balance discussion - they're an exploitative preflop range, therefore we should continue exploiting our opponent postflop.
But back to your question: honestly, I have no idea how my balanced betting range would look like in this case, most people cbet 100% in this situation, and if they don't, they're most likely unbalanced (having weak pairs like JJ-77, rarely K hi, rarely a random screwplay) - so I haven't worked on this at all. My first guess would be to bet the top30-40% of my range for value, and have an appropriate bluffing range. You should probably check back a couple of strong combos, so your checkback range wouldn't get all that capped, but in all honesty, I don't think it's super important you won't really be able to restrict Villain's vbetting range by all that much.
I put the nuts in quotation marks, suggesting I'd valuebet much less thinly than generally. And also, if we wanna remain balanced, we need to bluff as well. So saying "he should bet more" is level 2 thinking here - you think he thinks on level 1 (wants to get value), therefore you think on level 2 - however, if he knows you want to exploit him, cause he wants to get value, he will be pretty reluctant to bet. When I said "our range wants to get value" I didn't mean it in an exploitative sense, more just saying that a high range asymmetry situation demands us to focus on value much more than anything else.
My 3betting range is wide partially because of the reason I mentioned above, but mostly because opening ranges are wider these days. If you look at the PS SHC, I think it suggests something like 13% from UTG (and the 3betting range is based on that), while most people open more like 16-20% from UTG these days. But also having a tight 3betting range is always an exploitative adjustment, since your range will be really screwed up postflop, especially on A and K hi boards (see this example). Thirdly, you're 3betting from the SB in this example, which makes us even more prone to 3betting. Given all these, we may even widen it, but that would be my default range. QJs would be definitely in there, not sure why I didn't include that, JTs would be a bit of a stretch.
Also just a quick note: implied odds and playability are unknown concepts in balance (obviously it is included in our strategy).