Couple of other things to check out first, 88. First, do you have or can you borrow a chronograph? A broken spring or bad seal somewhere can cause lots of variation in shot velocity, and that will screw up any chance of getting good groups.
Second, is this your first air rifle? In other words, how much air gun shooting experience do you have? I find that an inconsistent hold on my part is my most common cause of bad groups, or stuff moving around. And it doesn't take much! Are you shooting from a bench or off hand? The Shadow I've used did best just rested on my left palm, and just touching my face and shoulder. Right hand, thumb and trigger finger only, NOT gripping the pistol grip. And if you're still using the stock trigger, either order a GRT from Bob AKA CharlieDaTuna, or try one of those new MiniGTX or whatever they call it. I haven't tried the Mini, but lots of guys on this forum have use the CDT triggers. I'm sure you've seen their posts. BTW, the Shadow mentioned above is box stock except for a CDT trigger. I've shot 1/4 inch groups with in on good days.
Most springers don't do well off sand bags, the CFX is the only exception I know of. The other question would have to be, how many shots so far? Some Gamos are notorious for fairly long break in periods. Defineing long as in excess of 1000 pellets.
Last thing I can think of is, are you still using the factory scope mount? I know you said you tried different scopes, but the stock Gamo mounts are not known for being especially robust. I've had good luck with Accushot by Leapers, both 1 and 2 pc. Around $15. Lots of other guys here like the 3 B's- B-Square, Beeman, and BKL. More expensive, but...
Finally, when you do get it tuned, I'd go with the Turbo. I think the minor extra cost is well worth having parts custom fitted to YOUR gun. Just my opinion, but hey, I'm at least a little smarter than the average bear...:-). Sorry I got so long winded, hope this helps.
Dave