Cause the OP asked about a balanced range?:)
I understand your problem, JL, however still have to agree with Dawnfall, in this situation thin vbetting/blockbetting is absolutely fine. Also, if you barrel the turn balanced (that includes turning A hi with a 9 or 8 kicker w/o draw into a bluff), you should have enough bluffs (namely 98s, A9, A8) to compensate for the fact that you're betting the river so wide. As you said, that card hit your range quite well, and you had the stronger range all the way, no need to have a huge, or in fact any checking range at all (if I bet 100% of my range here, I'm balanced in terms of vbet-bluff ratio).
Now one could say that betting our entire range on the river is pretty imbalanced, cause the opponent could wait till the riv with his valuehands, and not inclined to peel/fold anything. However this only happens on Q,J rivers, that the opponent cannot see ahead. It's just an unfortunate situation to him. If we wanted to be well-balanced in this spot, we should probably alter our preflop range - but in most situations that won't work out. That's the "beauty" of narrow range situations, that's why SH poker is a big pain in the ass GTO-wise (not to mention FR...). So in my mind it's kind of an atypical situation that comes up once every now and then, and you can't do anything else, just go with it.
The other alternative would be to check some (all?) Tx hands, and respectively check A9 or something from our bluffing range. We'd have to fold A9, and weaker Tx hands, and c/c with the rest. However you can see that this exploitatively is a bit of a nightmare situation for us, cause checking Tx is a negative freeroll in most cases, and c/f-ing a hand you'd exploitatively blockbet is another really big jump. That's why I'd go with betting our entire range, and be a tad bit more exploitable. And although I really really dislike this argument in most cases, in this case it actually might hold true: no one will exploit you for this.
Hope that cleared up most of the questions you had, if you have any other, don't hesitate to ask.