For the lazy of mouse finger , the space is 3.2 m wide x 5.6 m long with a 1 metre walkway down one of the long sides. Speaker positioning suggested is 2.1 metres apart on the short wall.
I would say four things:
1, Not all floorstanders are the size of old-fashoined red telephonephone boxes. Tannoys spring to mind, but there are other floorstanders around the 0.8 metre high x 0.25 metre wide size. Check out a few hifi shops in your area or the WHF listings for smaller floorstanders.
2, Your ideal soundstage should be (roughly and some will disagree) is with your listening position between equal to and about twice the distance from the speakers than the distance between your speakers. So, with about 2 to 2.1 metres, your listening position whould be about 4 to 4.2 metres (don't get the tape measure out, it isn;t that critical) from the speakers. This should work in your listening space.
3, Presumably you can't use the walkway space at all, so putting a speaker in the corner of the room within the walkway space is a no-no. If you could use the space, increasing the speaker separation might help. Having one speaker close to a side wall and the other in relatively open space won't be the best for the soundstage, as the long side wall may reflect sound from the left speaker as you have sketched the layout. It might be worthwhile experimenting with changing the layout putting the speakers against the long wall and you couch/sofa with its back to the other long wall or with its back defining the walkway space behind the couch. Is there a reason why the speakers can't be put along the long wall on the wall side of the walkway and the couch / sofa against the other long wall?
4, Floorstanders do not necessarily make for the best sound for a given budget. You may find a decent pair of stand-mounters give a sound you prefer for the budget you have in mind. The footprint, however, won't be much different. Wall brackets can be used, but I, personally would avoid them.