Band Joist on cantilevered floor joists

The issue that I have is that my house is 100+ years old. Had the stairs leading upstairs were not up to code. Bought a queen size bed, and can not get the box springs to go upstairs. Will try to explain this a lil bit. There are 3 2x8 floor joists that are running approximately 165 inches. This is right at the landing on my stairs, as my stairs take a sharp left. i know this is probably really general without pictures and so forth, which guess I need to do. But how much of the floor joist, could I trim off at the bottom? And yes, i am definitely worried about structure. thanks in advance

The facts: Home built btwn 1920-1940, balloon frame construction. home is TINY--3 rooms, 2 rooms on 1st floor, attic is 2nd floor, which is a tiny bath & bedroom. the foundation is about 11' x 24'--more like 10 1/2' by 23' when I measure in the bsmt My question is about the 2nd floor, which was actually a finished space from the time the home was built, so was 'grandfathered' in when inspected for occupancy. The floor joists of the 2nd floor are 2x6's spanning 10' 6" on the longest spans, & 16" OC. Joists are not true 2x6, but are close--the old heavy ones that are 2x5 3/4--old growth. Upon replacing the old cast iron stack with PVC, & pulling up the floor, we realized the old plumbers years ago had completely hacked through the joists under this bathroom. I mean hacked through, not just a couple of holes. The flooring on top of the joists was the 3/4+ tongue & groove pine. That tongue & grove appears was the only thing left supporting the toilet, aside from the old cast iron stack under... By some grace of god--this bathroom never fell through, didn't even have noticeable sag--despite the 3 joists in the center being utterly worthless. Now the issue becomes how to fix it. I understand no one uses 2x6 joists these days, because the wood available now does not have the same strength since it is not the old dense growth available when the home was built. I am VERY limited on what I can use to repair, because the ceilings below are only 7.5 ft, & the 2nd floor has minimal clearance as well, so using 2x8's would remove what little space I have. The only thing I can figure at this point that is in my favor is that the actual span is so small, I may well be able to use LVL's 1 3/4" by 5 3/4" sistered, I figure current day 2x6's wouldn't be sound for this application. Normally, I would jump right in & DIY--but I do not want to do it. I am actually waiting on a consult date with an engineer, which is a long wait, about a month, because it is a rural area & this is 'busy season'. In the mean time, I've got about a month of driving myself MAD trying to get ideas on how this could be fixed without taking away space from the ceiling below or above. I'd really like some ideas so I can draw some stuff up ahead, & present the ideas. I'm also removing the T&G flooring for access, basically 'prepping' it out so everything can be seen & accessed. I had one contractor in who feels it is not a huge deal, just a PITA job, & a small job, says he's seen this a thousand times in these old houses. I presented my idea of LVL's sistered the entire span of the joists. He thought spanning the entire joist wasn't necessary, & that lvl's would work well. He also cannot do the job for *several months*, so I am trying to get others in in the meantime, because waiting several months is not an option. I am personally stuck on spanning the entire joist with lvl & willing to rip out the T&G to gain access to have it done properly. Will put down 3/4' 5 ply subfloor when all is done. Other facts: the finish floor will be vinyl, not tile. Tub will be fiberglass, we pitched the old iron one, since it was so old the hole for the drain was too corroded to repair. I've had issues just getting contractors/carpenters to show up just to get estimates, since it is rural, out of the way & such a small job. Seems people do not want to work, or the job is not worth their time. 3 times just this past week, I've driven out there & waited & had "no shows". Nothing could be more frustrating--I drive an hour there, an hour back for nothing. Seems the ONLY way I CAN get someone to show up is to pay them, & I am so sick of contractors, I set up the apt with an engineer, but have to wait even for that. We might be stuck having to do this DIY, & I am not looking forward to it. For once I wanted to PAY someone else to do a job--and no one wants it. Thoughts? Anyone deal with this issue?