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Put it in a barlow or get a 2x corrector (which is just a barlow lens that screws on the end of the nosepiece). Maybe get a lower profile focusser or mod your existing one.
Even if you move the mirror up the tube, f/5 is too fast for a binoviewer with 20mm clear aperture and a light path of 110-120mm. You need f/6 just to fully illuminate the very centre of the field of view***. But that's not satisfactory. You need about f/10 or slower to get usable illumination. So get a 2x corrector to slow the lightcone down and then make the necessary alterations to the scope/focusser to achieve focus. If you cannot reach focus, the easiest way to remedy it is to add a straight 1.25" barrel extension (filter screw threaded at both ends male-to-female) between the nosepiece and corrector. Make sure the corrector you get has plenty of clear aperture (most barlow groups should give you 24mm, but I do have a 1.7x corrector that only has 10mm CA that makes it useless).
Another issue with moving the primary mirror closer to the secondary is that the size of the secondary will need to be increased to accommodate that. And if you do that, the larger obstruction will reduce contrast. If you don't do it, your secondary will not be fully illuminated and you're wasting aperture. So it's best to leave the primary alone.
[***This is a simple matter of geometry and there is no way around it: basically an f/5 "lightcone" will not fit inside a long narrow tube, i.e., with an aspect ratio greater than 5:1. And the lightcone not only needs to just fit but have enough spare room to be moved around laterally to illuminate a significant central portion of the FOV.]
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