I’ve once tested one of those jellies from Lush. Like so many things from Lush, they are very funny but not so useful and tend to break apart after a few uses…
Principally, the 50% glycerol is enough as a preservative but will eventually leak out from the outer layer and hence doesn’t help too well for surfaces preservation. By coincidence, I’ve just answered nearly the same question in another thread. Anyway, the things possibly growing on your jelly are likely those a bit harder to kill and you are well advised to use an efficient preservative (a standard combination should hopefully do). Read through these pages and related ones, you’ll quickly find a wealth of informations regarding this subject.
Yes, you have to adjust the pH to a range in which the preservative you chose actually works. Adding citric acid by principle will be a good idea as it acts as an auxiliary preservative and pH buffer.
Alternatively, partially replacing glycerol with propylene glycol will increase the self-preservative efficacy but again, the surface will remain problematic.
Regarding the anionic surfactant: Using a sulfate derivative reduces possible problems with a slightly acidic pH but they are rather aggressive (but clean well). You could go with a non-ionic one which will less interact with carrageen (how this actually affects gel consistency is up to you to try). Why not just use a pre-formulated blend?
You should read some books or do one of those online curses here . There’s no simple answer to your question cause it’s like ‘I have a metal tube and a stick and want to build a rocket. Which propellant should I use?’.
Now, there’s one you might try if you’re in for an experiment: Aminosoap by Ajinomoto, it’s a blend of coconut fatty acids and arginine. It has a relatively high pH, you should not use it alone in your formulation, and would need a preservative active in slightly alkaline conditions. The ‘trick’ behind it is less that of being a surfactant than containing arginine which at a certain relative amount with regard to carrageen (try 5% w/w and go from there) will ‘electrostatically cross-link’ carrageen resulting in a tougher, less easily breaking gel. Using too much will result in complete coagulation/precipitation of carrageen and your gel separates into its constituents. Be aware that this effect might kick in days to months after the fabrication! Finding the optimal proportion is easier with a slime rather than a solid gel. Alternatively, try pure arginine, lysine, or ornithine which you can buy ounce-wise for a few $$ and in pure form for example in body-building online stores. Small amounts of cationic polymers or divalent cations (magnesium or calcium) might work too but I suppose you’d only see the incompatibility manifest. Had that once with a toothpaste which was fine for several weeks before it ‘disintegrated’.
Or play around with mixtures of different gelling agents. They have often better properties than the pure ones but there’s unfortunately no way around testing all the possibilities by yourself. Personally, I’d try a mix with gelatine first… if you use sugar instead of glycerin and raspberry flavour to replace the rest, then you get an edible Jelly-O and won’t have to throw it away if it isn’t perfect . Sure, sugar will behave a bit differently, but to get a feeling for the mixture, it’ll be close enough.