I am making my own wiping varnish by following Bob Flexner's recommendation of mixing polyurethane varnish (in my case, Minwax semigloss) with odorless mineral spirits.
Without realising it you actually haven't followed Flexner's advice exactly, see previous Answer, noting carefully the wording of his very first bullet point.
Flexner recommends using gloss varnish exclusively for the build coats with wiping varnish. The main reason1 for this is that any varnish with a sheen less than full gloss has matting agents, which fall from suspension and must be continually stirred back up to get even results. And the thinner the liquid the more quickly settling occurs.
So using semigloss is likely to be part of what's causing your uneven results, but obviously your varnish mix is drying a bit fast too.
When varnish tacks up too fast one solution is simple, just add more solvent. You mention you've tried this already but you can go further, in fact as far as needed — Flexner has pointed out in his writing that there's no limit to how much you can thin oil-based varnish and it will still dry fine. So with an atypically fast-drying varnish you could mix it 1:1, or even more dilute if necessary.
Your workshop is not warm and you're using an 'odourless' mineral spirits or OMS, which is slower evaporating than standard MS or naphtha2, so you're already ahead of the game here.
For next time
One other key aspect of using wiping varnish is wiping away the excess. You don't have to, you can wipe away all, some or none of the excess varnish and it will still dry normally (although the time taken will vary). But you're more assured of a very nice surface that doesn't need a lot of work if you wipe much or all excess away, although the varnish will build more slowly this way, requiring more coats e.g. more than five3.
What to do now
You're already at 6-7 coats, you've likely got a decent build already but the surface isn't as smooth as you'd like so you have to work on it. One of the standard ways is 'flatting off' AKA rubbing out. To begin with you need to wait for the varnish to get good and hard. Many pros wait a fortnight or more before doing this, not just a few days to a week.
After you're done with the initial flattening stage, commonly done by sanding wet, the surface will be very flat but very matt and you proceed from there to get to the finish you want.
There is much good advice online on rubbing out varnish and other finishes, so just as a sample, Rubbing Out Finishes on the Homestead Finishing Products site (written by Jeff Jewitt). It's light on pictures, actually there aren't any, but it's longer and more detailed than many guides you'll find not protected behind a paywall.
If the surface isn't quite as bad as I'm imagining the simpler technique in this video from American Woodworker may be all that you need to employ, Fast Finish Rub-Out
Note: normally you'd do this with gloss varnish. The matting agents in semigloss may cause a problem. But the only real alternative is stripping back to bare wood and beginning again.
1 Another reason is that multiple coats of satin and more matt varnishes build up a certain ghosting or cloudiness, obscuring more of the natural colour and grain of the wood than is desirable.
2 Do be aware that in addition to the reduced smell OMS has a weaker solvent action. This can cause issues with finishes such as varnish that contain resins and also makes it less effective as a brush-cleaning solvent for these finishes.
3 With no upper limit. You can apply a dozen or 15 coats if needed and have the patience.