Low profile 28mm tyres

i had that issue  with gp4000 s II's on an oltre XR4. schwalbe durano 28c fit with room to spare.

Conti 4000s are very tall tyres but they are also very wide, 25s are 28mm wide on my rims. (18mm internal rims). 

what are the internal width of your rims? IMHO, 28mm tyres are really optimal for 21mm internal width. Even 19mm rims perform better with 23mm ones (those will stretch out to 27-27.5mm anyways. At least I've measured bontrager R3 tyres on 19x622 bonty rims to be 27.5mm by caliper)

the lightbulb looks ridiculous, 28mm tyres are more uncomfortable on the same pressure as 23mm ones and they behave very weird during cornering.

Rule of thumb: rather than switching to wider tyres, you should switch to wider rims (ie.: KinLin XR31, Hunt wheels etc..)

IRC make low profile tyres that are true to size. The only issue is that most of their tyres are quite expensive and they're also mainly tubeless. 

The Cycle Clinic who are the supplier of IRC tyres in this country have all the dimensions of the tyres when inflated on their site. It was invaluable for me as I needed low profile 25mm tyres that would fit under mudguards and went with them. So far I can't fault the tyres:

https://thecycleclinic.co.uk/collections/road-tyres

I would imagine that a wider wheel would lower the tyre profile, on the basis that the rubber would be pulled wider, if that makes any sense.

Sorry, can't help on the tyre... though I will say that the 25mm Conti GP4000 has a nats chuff's clearance between it and the seattube cutaway on my Argon18 Nitrogen.

i couldn't fit grand prix 4000's in 28mm on my supersix or my tcr, 28mm vittoria rubino pro's (the old non graphene version) fit both bikes,if you can find them in 28mm they're worth trying, though the newer graphene range seems to have usurped em !   

I found 4 seasons were tall too, I ended up buying some Giant P-SLR2 tyres in 28mm (circa 280g) and though coming up at 29mm wide on a pair of '01 Mavic SSCs they fitted just fine on my carbon bike. Problem is finding the 28s are nigh on impossible, not sure what Giant's newer range are like tbh.

Rolling resistance found the 28mm 4000 to come up at 29mm in height whilst the 25mm came up at 25mm on a 17mm wide rim, that 25mm tyre also measured 27mm wide when inflated. The Vittoria Corsa G+ is 24mm in height for a 25mm and that comes up at 27mm on a 17mm wide rim to. I bought a 28mm for when I wear out the Giant's but haven't fitted it yet though it weighs around 270g so only a few grams lighter than the PSLR but the vittoria is certainly thinner at the tread even than the conti 4000 and much less thinner than the Giant.

Wishing now I'd bought a dozen of the Giants at closeout from Rutland!

Conti 4000s are very tall tyres but they are also very wide, 25s are 28mm wide on my rims. (18mm internal rims). 

Conti tyres often seem to come up a little larger.

My 28mm GP 4 seasons come up just short of 30mm and my 25mm GP 4000S's come up just over 27mm.