Lots of opinions here. most of which I concur with.
Firstly, but unrelated to your staining problem: You seem to have confused the fixing procedures needed for fiber-base paper with those needed for RC paper. You don't need a two-bath fixing regime with RC paper. If you follow the Ilford fixing method of using Rapid Fixer at the 1+4 dilution, 30 seconds is all that is really needed. However, since there is no chance of fixer soaking into the paper base, a bit longer won't hurt. I can't imagine that your 45 seconds would degrade the image appreciably, if at all. The second fix is simply not needed. Do follow the manufacturer's recommendations for capacity. Really, though, think of RC paper more like film; it's only the emulsion that absorbs any chemicals; the base is non-porous. For that reason, the processing of RC paper is more like film than paper.
Now, if you're not using a rapid fixer (you don't mention which fixer you use), but use a powdered fixer (sodium-thiosulfate based) then you will, indeed need to fix longer. Again, follow the manufacturer's recommendations for time and capacity. And, if you are using a different dilution for your fixer than the "film-strength" dilution of 1-4 (or whatever, if you're not using Ilford Rapid Fixer or Hypam), then you need to fix longer. How long will be in the instructions.
Dektol usually needs longer than one minute to do its job. If you like the tonalities you're getting at one minute it might be because you're "snatching" the print a bit early from the developer, i.e., before development reaches "completion," which results in a bit less contrast and a warmer image tone. If this is what you're liking, then you'd be better off with a warm-tone developer to start with. Do a bit of research on warm-tone developers and try one.
Personally, I'd stop for longer - at least 30 seconds. Not stopping the developer completely could be the cause of your staining. Active developer carried over into the fix often causes staining of the emulsion. This would be the first thing I'd try to eliminate the staining.
When you say "Hypo," I'm assuming you mean Hypo Clearing Agent or some other kind of wash aid. Again, these are not strictly necessary with RC paper, but they won't hurt and will reduce washing time a little. And, don't worry about carrying a wash-aid like Hypo Clearing Agent into the second fix; it's just sodium sulfite and won't hurt the fix in the small amounts that get carried over. Still, it's not needed before a second fix and a second fix isn't needed at all for RC papers. Save yourself some time and space and just use one fix at the proper dilution for the proper time (and capacity).
If extending the time in the stop bath (and do use an acid stop at the recommended dilution) does not cure the staining problem, then the problem is likely with your Dektol. There have been problems with Kodak chemistry lately. I've stopped using just about everything from them except Indicator Stop and Rapid Selenium Toner.
If you like the tonalities you get from Dektol, try Ilford Bromophen. It will last a bit longer, give a bit better shadow detail and similar image tone to Dektol.
If you really like Dektol better, then mix your own. D-72 is easy to mix and has just a few ingredients, which, once purchased, end up being lots cheaper in the long run. I mix D-72 and ID-62 from scratch with simple spoon recipes. I'd be happy to share them with you if you're interested.
Oh, one more thing just occurred to me: Maybe you like the highlights in the image just because they are stained? That would give them a warmth and a bit of a "glow" like old warm-base papers had. If so, try Foma papers; their emulsions are a bit warmer in the whites even though the paper base is still "white."
Hope this helps,
Doremus
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