Shimano Charts
Remember that Shimano compatibility are based their expectation that you may be cross-chaining a drive-train as shown in the illustration below. Their charts ALWAYS allow a drive-chain to cross-chain as they do not know the experience of the rider that the bike is being sold to at the point of manufacture and design.

This illustration above shows improper shifting and no experienced rider ever does this.

This illustration above shows proper shifting on a triple . You can imagine from this that even on a double crank that proper shifting would never be in a cross-chain situation.
Derailleur-Cassette Compatibility
That being said, I have fond that you can almost always increase 2-3 teeth on a low cassette gear. As Nathan said, you may be able to squeeze and 11-30 on with a b-screw adjustment to maximum. Being a 105 you may be able to get 11-32 as the lower derailleur models like Tiagra and Sora do not have as well designed parallelogram as the upper levels. For instance, the Sora line from 6-8 years ago had a problem doing more than 2 additional teeth comfortably but since models changed last year with the addition to 12 speed, Sora is now a redesigned Tiagra derailleur that in most situations could comfortably increase a cassette by 3 teeth. So not only the model of derailleur but also the years or age of it makes a difference as well. Derailleur hanger position/style to dropout position plays a roll and and sometimes 1-2mm can make all the difference in whether it works or doesn't.
Capacity Solution
As for capacity, you could solve some of this by eliminating the smallest front chainring or adjusting the front derailleur stops from allowing it to drop down to it. Triples have been deprecated for a reason and even with an older 8 or 9 speed, a double allows enough combination to get up the steepest of hills unless a person is very out of shape and in that case it would only take riding on flatter roads for 2-4 months to build up the strength. Pro racing setup did not have triples even for mountain stages and these triple cranks were primarily for touring setups where one would have panniers and cargo going through mountain passes.
All of this information is not only taken from my own experience, but others and many quotes on the web to back up the notion that.
You would do well to google Sheldon Brown as this guy has a knack for modifying and customizing bicycle equipment, namely drive-trains apart from the documented, working methods and standard and getting them to work smoothly. He has actually talked about this very subject and has many a plethora of online documentation and guides.