Before glueless floating wood floors, you had to use a PVA type II adhesive, on the tongue or in the groove, and the use of strap clamps to compress, for a tight fit. Properly milled flooring capable of gluing t&G are still made. Not all engineered can be floated. Some have to sloppy of a T&G to do so. Those are usually gluedown only.

And just to be helpful (probably not...but here we go), a 5" wide hardwood needs "glue assist" with a nail in place install. So there must be some gluing going on. The extra cost of the sound reducing membrane isn't what is driving the cost up. It is the two layers of glue (yes the acoustic underlay must be glued and then the hardwood glued over top = double stick) and the extra labor to do everything "twice". Twice the labour, twice the glue = twice the budget. A glue down hardwood is the most expensive form of hardwood install we have. Nailing is the cheapest. A floating method is between the two. A glue assist for a wide plank (ahem...5" ranks as wide plank = needs glue assist) is more expensive than a float...but not as expensive as a full spread glue down install. Check to ensure the quote for the nail down includes the glue assist. If it doesn't, then they could be missing a step. The 1/4" cork underlay (from iCork Floor) = $0.66/sf. Some shipping costs (maybe $0.45/sf) brings it to about $1.10/sf for the cork. The other $5/sf is the glue (assume $1/sf per layer = $2/sf) and the extra labor to do all this gluing. The material only adds $3/sf. The labor is the other $3/sf. $3+$3 = $6/sf for this install. If you MUST HAVE acoustic insulation + solid hardwood, then you must have the extra $6/sf. There is a possible solution: floating hardwood. Yep. Float the hardwood (very few solid hardwoods are allowed to float...so you need to look at engineered for this) and you FLOAT the cork underlay. No glue = reduce the material costs by $2/sf. Since floating a hardwood is just SLIGHTLY cheaper than a "nail + glue assist" install, the cost of labor for the floor itself won't change. Switch to an engineered hardwood that can float and then add the 6mm cork underlay. It will add $1 - $2/sf to your current quote. My calculations indicate you have 2500sf of flooring. The cork underlay will only add $2500 to your material costs. Compare that to $15K for the double stick total. The solution = floating engineered hardwood. You can have your cake and eat it to.

First, I'd use a single edge razor blade held at about 10 degrees off the surface to shave off most or all of it. Second, if anything remains, I'd use something like this: https://www.homedepot.com/p/Goof-Off-4-oz-Super-Glue-Remover-FG677/204055736 Third, I'd quit using the countertop as a work surface for crazy glue.

Just circling back to testify to the efficacy of the teabag method. In general Sally Hansen's Repair + Rescue has helped strengthen my nails overall, but I really needed something more for my thumbnails, that had vertical splits that just wanted to keep splitting. I tried a couple of glues, but the one that's most effective is one for artificial nails KISS PowerFlex Maximum Speed Nail Glue, about $2 from Target. I cut a tiny square from a teabag (one will last a lifetime), put a tiny drop of glue on my nail, place the teabag paper on top. If it doesn't completely saturate, I put a tiny drop on top. Let it dry completely and then trim whatever sticks over the top and buff down to a somewhat smooth surface. Over that the Repair + Rescue and it holds for 2+ weeks. Meanwhile I gently file down the length as they grow. It's gonna take another couple of weeks and I should have the split entirely grown out.