I'm doing this right now.

I apply the glue while the record is spinning, and spread it with a credit card type plastic card. When it's dry I use a scalpel to lift it from the inner side of the LP (I insert the scalpel between the glue and the record). Then I easily peel it off with my fingers.

On a very dirty record, 4 gluings per side usually halve the amount of dirt.

This process might get most go the dirt out but scares me. I have used wood glue and did not clamp my work, after the glue dried I noticed the two pieces were separated a little more then the way I left them. I could be wrong but it seemed to me the glue expanded a little and if that is the case what would it do to the record groves. If you have a nice record collection, invest in a good vacuum machine.