I can definitely see you noticing the jump between 25 and 27. But between 27 and 28? Not so much. The larger you go, you need more of a tooth difference to get as big of a jump in gear inches as you do in smaller cogs. Does that make sense? You can look on the Sheldon Brown gear calculator, plug in your little ring size and then compare the gear inches for a 25, 27, and 28 cog.

I don't think you will have any shifting problems putting on a 28 with Shimano. You will need a slight adjustment of the rear derailleur perhaps, but it's definitely compatible. I've ridden both sram 12-28 (with shimano) and shimano 12-27, and the shifting is fine. Now I would use a SRAM or KMC chain with a SRAM cassette, but those work with 105 fine. I've heard that SRAM chains don't mate super well with FSA cranks.

I don't think you'll notice a big jump in shifting ease in the front between Ultegra and 105 on a triple drivetrain. Most of the issues getting a triple to shift cleanly has to do with the nature of the triple more than the front derailleur. I have moved from 105 to Ultegra on the front with a compact, and they perform the same. I have noticed a difference with Dura-Ace, but I think some of that has to do with the Dura-Ace STI levers (different throw force and throw length). BUT you may notice you have better shifting with a stiffer crankset, particularly under load. I can't really judge Ultegra triples (my friend has one that works just fine), but I know that there's a big difference in feel between Dura-Ace and 105 from my personal experience. Shifting is crisper. The biggest difference, especially for triples, would be in the feel--the power transfer and acceleration feel. So maybe you'd get hooked on better components, but they aren't necessary if you're happy with 105.

As for your mountains dilemma, I know exactly what you mean. I live in an area where I do just fine with a 50/36 and a 12-27. I can even travel nearby and hit some more hills. It also serves me well for racing in my area. Sometimes, we like to take training camps to the mountains, and I run out of gears and stress my knees climbing for 7+ miles with some grades in the high teens to 20s. My plan was to build a training bike. In case I didn't have the cash for more wheels (and since I'm pretty maxed out on the cassette anyway like you), I thought I'd just go with a 50/34. The little ring would be obnoxious for flatter training, but I'd have a good range for the 50. It could give me that little bit of push I need to keep my RPMs up when the grades increase. But now I've been offered a frame that would be better for racing, and I'm even considering a standard crankset. I may buy a 34t ring for my other crankset in that case and just put it on the couple times a year I hit the mountains. If I was going once a month, then it'd be on there for good. So maybe the climbing bike would be worth the cost.

In that case, you could even stick with Shimano and use a lot of parts from your current bike and still upgrade your "good" bike if you want.

If you stay away from carbon fiber levers etc. the highest end cassette and chain, you can still be in the cheap repairs range. For the crankset, you may eventually want to change rings. High end rings are more expensive, but it's not like a $700 carbon fiber finish RD (DA7900 or SuperRecord). Maybe put a compact double on the current bike and move the triple stuff to the climbing rig. The possibilities are endless.

I agree having a backup bike sounds like the best for your needs because you don't want to be swapping your derailleur once a month, and it doesn't seem like you need rear mountain gearing the rest of the time.