I suggest putting it in a hot car until its really hot, like you can barely pick it up. then slide a very thin piece of plastic around the edges and take the whole screen off. (I did my 1st gen surface pro this way. ) Refer to the disassembly guide or tear-down to make sure you don't damage the cables. (for the first gen, separate the sides and top with the plastic card (you want something thinner than a credit card actually, like perhaps a piece of a milk jug or water bottle) Then til the screen up along the bottom edge. Do it SLOWLY and a little at a time and the glue along the lower edge will separate. Also, once the screen is free, let the laptop cool COMPLETELY before undoing the plastic clips that hold the FPC cables down.
When hot its easier to break them. CAREFULLY clean off the old adhesive. Its a job that will take a few hours. Don't rush it or you will damage something. Use some 3M 9448A black double coated tape to put the screen back down. This will result in a much more professional and permanent repair than gobbing liquid glue in the gap and smooshing it down. While your in there, you will likely want to replace the solid state drive. A 250GB samsung msata (for first and second gen units) or m.2 (for 3rd and 4th gen units) can be had for around 80 dollars. A 450GB drive can be had for around 130-150 these days. Since your in there, you might as well do the upgrade since once you put it back together there is a good risk of damaging it if you take it apart again.
Remember though, ANY time you take apart things like these tablets, there is a risk of something going catastrophically wrong. If you have deep scratches on your screen for example, don't even try it, or it WILL break. (right at the scratch) Another problem is the fpc cables that connect the screen. The battery has to be connected when you assemble and disassemble it. As such, if one of the FPC cables is crooked going in or out of its socket, it will short out and you will let the magic smoke out and that will be the end of your tablet.