Across the 24 gears on your bike there are a lot of near duplicates. There is no need to ride with the chain on the big ring if you are then using the largest cog on the rear.
From what I remember the triban 3 has a 50-39-30 chainset and a 12-13-15-17-19-21-23-25 cassette. Assuming these figures then you get the following gear inches for each combination: -
Wherever the numbers are the same then that gear combination will feel the same on the road. By the time you are down at 50-25 then 39-19, and the chain line will be a lot better.
To change the groupset on the bike you are looking at well over the price of the bike new, and even just to change to compact would mean new chainset, front mech and STI, which will cost a decent proportion of the bike's value for little more than vanity. IMHO it is not worth it, just learn to use the gears more sympathetically and you will be fine.
Oh and for the record, I have two bikes with 2300 triples on them, between them they have been ridden for over 12000 miles without an of the problems you describe.