I've got some gorilla wood glue somewhere, should be OK with biscuits?
Absolutely the wrong glue! You need a water-based adhesive, something like EvoStik Resin W D3 (blue bottle). The reason is that biscuits are extremely dry and are made by compressing in a hydraulic press - so that when you add water based adhesive they expand to fill the grooves and lock the components together. PU glue isn't water based and doesn't do that. Leave any sanding for 24 to 36 hours in order that the glue sets fully and any moisture trapped in the MDF has a chance to dissipate. If you sand too early the biscuit shapes can telegraph through to the surface of the MDF and show when the surface is viewed in an obtuse light. This occurs because the biscuits swell then slightly shrink as the water content of the glue dissipates into the surrounding MDF material. A bit technical, but can sometimes be a real issue
Normally with biscuited joints you need to cramp the joint until it sets. Obviously that is impossible in your scenario - you may need to consider using some small screws through the joint until it sets which can be removed, 2-pack filled and sanded after the glue has cured. We sometimes need to resort to this on site. At the very least pull the joints together with masking tape - you want to avoid having to 2-pack fill the joints if at all possible.
Cheapest way to slot for biscuits is a biscuit slotting bit in a router - providing you have a router, that is.
Additionally, as this is a window board, and it isn't MR-MDF(?), I would strongly recommend that you seal the edges, back and bottom (i.e. the bits you can't see) before you install the board. An oil based primer, some old oil paint or something similar will do the trick. Window boards are often subject to high moisture/condensation and major variation in temperature throughout the day and the year and you want to avoid the MDF wicking-up moisture (and for that reason commercial window board is normally MR-MDF and comes pre-primed)
Because window boards are subject to swings in temperature and humidity adhesives like GripFil, Pink Grip, etc aren'talways reliable. We used to level the window boards front to back and end to end on packers, then drill through the top and (SDS drill, plug and) screw through the packs of packers to hold them in place (the countersunk holes were then either pelleted or filled, depending on the base material). In recent time s we have instead sometimes moved over to using the same sort of expanding foam you use on fire door casings (i.e. low expansion) to fix the boards. They still need to be packed-up level first, though, and may need to be weighted down until the foam goes off. Any discrepancies in plasterwork beneath the window board is made good after the window board is properly secured