I travel on Eurtotunnel regularly (like 70+ single trips in the last 2 years [8|]). 9 times out of 10 the staff will realise that you cannot go on the top deck in a GT3RS and will direct you to the lower level. If they don't, simply point at the lower level and they'll realise and oblige, as others have said before.
However, also as others have said, you could book as a high car and get a bit more clearance either side as the distance between kerbs is wider as well as there being no 'upstairs' level. You go through the 'higher than 1.85m' lane and join those vehicles that are higher than 1.85m (including coaches, but not including lorries - they go on a separate 'open-sided' train).
You'd be fine on the lower level with a 'normal' booking. My old Elise was 100mm at the front and had no trouble (albeit with less front overhang than your GTSRS), but for extra width and the reassurance that brings, you could book the >1.85m. Only downside is that you have to walk further for the loo as they're in 1st and last carriages, whereas they're every 3 carriages in the 'normal' double-decker config.
I didn't take the Elise or now my 997 on ferries for the ramp angle and coat zip/handbag scratching issues (there are some selfish s0ds about, aren't there?!). Eurotunnel is 100% more suitable for both reasons and a much quicker crossing to boot.