Try going to a carpet supplier & see if they have any cheap remnants of lino, you could put this on the base of the run, cut it so that it slopes up the sides a little too (I expect the 3cm you mentioned would be about right?) overlap the corners of the lino where you cut it&there should only be a tiny hole for liquids to seep thro.
Try a puppy pad in each corner under the lino to catch any leaks if easier? (this should also protect the wood from chemically reacting with the urine, I think this is the main issue with pine... But I'm not sure?)
Maybe just seal the overlapping edge with waterproof duct tape/wide insulation tape & tuck in the top end between the lino & wood to make any loose ends less prone to chewing?
With the upright struts, are they of a size that trunking could be slipped over the bare wood on the insides if they like to chew?
Something like this..
Maxi Trunking 3m 50 x 50mm
Or the smaller mini trunking if the wooden struts are small enough?
Mini Trunking 3m 38 x 25mm
You could get either from a DIY shop, building supplies or electrical suppliers.
To be honest my guineas have never really chewed wood, one of them now has a nibble on their plastic pigloo, but generally I've not had a problem with chewers. Not even when I had a wooden run about 15+yrs ago.
Its a lovely looking cage can't wait to see it with Guineas in it
