I don't think you will need to disconnect the links. You can lift the 3 point anytime and the mower deck should remain down. There is nothing forcing the 3 point down other than gravity and weight. Done that more than once in a pinch or by being stupid.
Well Eagle1 in response to your emphatic statements I did try something I'd never tried b4 on the BX1500.
I pulled the lift control LEVER all the way back to lift both mower and tiller, and turned the lift control KNOB under my right hand to lock everything. I think I turned CCW to lock it, not sure now. Anyway at that point tiller and mower were locked inthe highest level.
(I don't think the "TOP" position on the mower height control has much to do with these things, I may be wrong.
I still thought they were completelty connected. The only control I had to use was the lift lever, so I let it down a slight bit. By gosh and by darn, the tiller stayed sort of all the way up but the mower dropped more than I thought it would. I don't know if it's enough for mowing or not but I will certainly try.
Evidently as you said there is some individual "dropping" available for the mower.