There are a few aspects of your guitars setup that make it not ideal to have to switch tunings. My personal instrument (bass) can take many tunings to a point as the strings are more robust, but you end up with a few issues around the action (the angle of the neck relative to the body, which causes the fret buzz), the nut width and possibly the bridge setup. It's not really ideal, and it's less important for me as chords aren't a concern. There's generally a way around whatever I'm trying to do. I play guitar less, but have run into the same problem.
My guitar strings are a lot more temperamental than my bass ones simply because they are thinner and have a lot lower tolerence for changes in tuning. I know you ruled out a second guitar, as ultimately that is the best solution, but you are trying to cover an awful lot of ground on one guitar. On guitar the only change I'll really do is low E->D as anything beyond that affects the tension and tonality too much. On bass I tend not to, but have been known to go down a semitone on the lowest string if I really feel I need the extra range.
I find changing the tuning too much can affect my playing as the patterns on the fretboard shift. If you're happy with moving the tunings to play then I would suggest:
I know you ruled it out, but for the large range you're trying to cover a really cheap second guitar would reduce the strain on strings constantly being retuned, provide a potentially better setup for a different tuning and save you time constantly retuning while practising. If you get two you can cover more ground and have strings specifically for higher or lower tunings. A professional musician will have loads obviously, but for £60 you can get a guitar just to practise on, with a more serious instrument if you need it. It won't be best quality, but may save you money long term with the strings you'll be buying constantly by increasing/decreasing tension.
Failing that I'd tend towards strings that are lighter than a middle ground. Whilst having strings too loose isn't ideal I would say it's more optimal than trying to increase the tension beyond what they are designed for. You do have to be careful of not damaging your current guitar as the neck won't be that happy with constantly changing tuning.
Without knowing the songs you're playing/writing it's hard to say, but possibly look at playing chords elsewhere on the neck and staying in one tuning. If you're covering songs they may sound different so that's your decision to make.
Ultimately, there's nothing wrong with retuning constantly, however in your case the amount of ground you are trying to cover is quite large, which is what will cause problems.
Just a quick update as I checked what I have on my bass on the moment as an example. I have strings of gauge 35, 55, 70, 90 (If I remember rightly) tuned to EADG. I prefer really light strings for ease of bends (yes, on bass...) and slap bass, but it does mean I won't be able to drop the tuning too far. What I mean about the setup is that the action and such is set up for these very thin strings, and trying to drop the tuning will make them far too loose to play properly and will sound dreadful.
For comparison I also have a really old bass on BEAD tuning. The thicknesses there are something like 75, 95, 110, 130 (they're really old so can't remember exactly). I would not want to push them into higher tunings really as they are already pretty tight. I don't really play this one that much. I might change it to DADG or something instead as I rarely use C# or lower.
This means my two different basses have totally different actions, bridge settings and the second has an adjusted nut to accout for the thicker strings. Rather than trying to have one bass in the middle to try and cover both it's far easier to have two. The first is a (soon to be replaced) Fender P Bass and the second a cheap Ibanez BTB200, and realistically I never gig with the BTB.
This is quite a bass-heavy answer, so I texted my guitarist mates to see what they said. One generally doesn't change tuning, but has a cheap second guitar (his first one that got replaced recently) if he really needed to. Another doesn't go far enough from EADGBE to really need a second, but he does drop the low E to a D occasionally. He prefers to use a capo and find other ways of playing the chords. He said he would like to, but the second guitar would have to be gig-worthy. He often uses weird tunings on an accoustic to experiment though.
The basics of setup will carry over from bass, but I'm aware alot of these tunings are based on the open string notes, which I avoid at all costs on bass unless truly necessary, having lots of song specific tunings are perhaps unecessary. Hopefully there is some use to be found in all this.