Good tips thus far, make sure you allow a gap that is large enough....i would use a thin paperclip for your shims. One thing to consider for thick material is the weight and the amount of time required to properly melt the two pieces. If you use a really thin shim(it could break when you go to pull it) the vertical piece can and will make contact with the adjoining piece because the shim will melt into the plastic creating such a small void that the plastic will prematurely join prior to you pulling the shims. Another thing to keep in mind is the enviroment around you. Make sure the room you are doing this has proper ventilation and is cool(72-75f) and very low humidity. Once you have the pieces jigged up, raise the vertical piece a 1/2" and prep both the edge and the adjoining face with acetone to remove all finger prints(makes the solvent run funny,airpockets). Remember, you only get one shot! Good luck
PS make sure to use the thin,smaller paper clips. You will need one on each end and one in the middle for a ten foot span(sagging). By the way, why do you need a three horse router to cut 1.25......horsebucky. you cant get perfectly smooth edges with no chatter with a 3/4 horse with the proper carbide router bit(designed to cut plastic, not wood) all it takes is a steady hand.