I'd say there's 7 contenders. Stich, Roddick, Medvedev, Muster, Thiem, Gerulaitis, Delpo.
When considering 1-slam winners, you need to think about their finals (possibly semis), plus their opponents in their deep runs. Other considerations are their total trophy count, matchup history against their best competition, and the amount of Masters-level trophies they have (plus DC/YEC/Olympics).
In terms of slam statistics, Thiem/Roddick/Medvedev are all on the same level. 1 win, 4 finals, multiple semis. Roddick slightly ahead for his additional semis, not to mention playing all his finals (save the one he won) against a peak Roger Federer. I would then say Stich (very good win, but I'd argue his losses aren't fantastic and there are fewer of them to go off of). Slightly behind is Gerulaitis for me (simply for the weak 1977 AO), despite also having 2 finals and 5 SFs. Then Delpo then Muster. Muster really underperformed the French for how great he was in the premier clay tournaments.
In terms of non-slam stats, Medvedev and Muster have their own category. 6+ Master-level tourneys for both. Muster has 8 (+ a ton of lower level trophies), but Medvedev has 2 DCs and a YEC. I'd say Med first, Muster 2nd. Then Roddick (5 Masters, 1 DC), Gerulaitis/Stich, Thiem/Delpo. Everyone has roughly 20 titles other than Muster (44), Roddick (32), and then Gerulaitis (26).
At this point, Delpo probably falls off the list. Even a fantastic top-level matchup history wouldn't save him. I realize he got unlucky with injury, but that's life. We can only consider what he actually did do, not what he could have.
For matchup history:
Gerulaitis (vs Connors 20.8% out of 26, vs Borg 0% out of 18, McEnroe 21.4% out of 14). Tough to consider him, and with no stellar slam or non-slam stats, I wouldn't consider him further.
Muster held his own in matchups. (vs Bruguera 80% out of 15, vs Edberg 0% out of 11, vs Sampras 18% out of 9) are the standouts, went roughly even with Agassi, Moya, and was very positive against former #2s Corretja and Chang.
Stich was roughly even with almost everyone of note. Fell a bit behind Becker/Courier/Kafelnikov, but not massively (around 30% wr), even went positive against ATGs Edberg, Sampras. Just not against Lendl, who beat him 6/7 times. Still, very strong.
Roddick was terrible against Federer, far and away his greatest rival, but had mostly positive (or close to even H2Hs) against most others he went up against. Only pitfalls (30% or under) were Federer, Murray, Nadal, Agassi. Very strong people to be losing H2Hs to.
Medvedev is also generally positive with only really 3 tough matchups. Djokovic, Bautista Agut (?), and Nadal. Djokovic and Nadal are understandable, but most of that has been in their old age. And with no significant trend upward recently, that's a black mark. However, he is only underwater on 1 other matchup he has more than 5 matches in - Mannarino, with whom he's 3-4. Medvedev clearly doesn't have many bad matchups either.
Thiem had his good days and bad, clearly. He's near even with all of his 12 or more time rivalries, but it gets weird below that. He's 9-2 against Simon, 3-7 against Goffin, 2-7 against Anderson, 2-5 against Rublev, 5-2 against Federer, 2-3 against Murray, 1-4 against Verdasco. And ALL of those (save a loss against Murray) happened before Thiem's injury and rehabilitation. Very strange.
Conclusion:
I don't think Muster's fantastic non-slam results save his lack of additional slam finals and deep runs in general. He did great, really, but how many 250 wins is a slam final worth? It's tough to say but seeing Muster have no YECs, no DCs, a R1 Olympics, no slam finals except his win, I don't think it'd be fair to say he's the greatest 1 time winner.
Similar goes for Thiem. He held his own against the best, but went on walkabouts against the worse players. Fairly bad records there, and the other records weren't stellar to make up for it - they were also mostly even. Just being a decent speed bump for the top players doesn't mean much if you don't parlay it into more slam wins. Lack of consistency (save for RG) probably takes him down a peg, though he did face Nadal at RG several times to get his losses. He's still high, just not #1.
That leaves only Stich, Roddick, Medvedev. Roddick > Med > Stich in slams, Med > Roddick > Stich outside slams, Roddick > Stich >= Medvedev in H2Hs. You could also do a subjective ranking of their levels in general, but I don't think I will, seeing as I didn't watch Stich and would probably be biased against him in that regard.
I'd say Roddick is the greatest 1-slam winner ever, followed by Medvedev, then Stich, then Muster, then Thiem. Beyond those 5, I think it'd be fair to consider Chang and Orantes as well against Gerulaitis and Delpo.
TLDR: Roddick, Medvedev, Stich, Muster, Thiem.