7.5 x54.5 Swiss is interesting. Iirc, it and the French 7.5 both use .308" diameter bullets.
The x55 Swedish has a slightly larger diameter than the x57mm Commission and, 06 families of cases.
The x54.5 Swiss is slightly larger again.
That body diameter is slightly larger than the 7.62x54 Mosin Nagant, and if the rims are turned off, Donelly claims that 7.62x54 brass can be reformed to make slightly short necked Swiss cases. I think that case head bulging would be nasty, if that was tried for full pressure loads.
In the factory/ military case, capacity is about 63 grains of water, so mid way between the .303, .308, x57mms and the x64mm, 06 cases.
Back in the 1950s and 60s, a Dr Arch developed loads for a series of wildcats from .257" upwards, based on the X55mm Swedish case, blown out a little. Ackley's books list loading data. IIRC, Dr Arch was interested in heavy bullets. Dr Arch's other well known project was the .378 Weatherby necked down to .30 for 1,000 yard target shooting.
Arch's work will give you some idea of what the wildcats will look like. For performance, given the same operating pressures, bullet weight and calibre, and barrel length, they'll be roughly mid way between .308/x57mm based cases and 06 based cases.
Slightly larger case head internal diameter will mean approximately 50% more backthrust against the bolt for any given peak pressure, possibly giving slightly more dispersion of the groups compared to .470" diameter cases. This last point is based on the reasoning given in Harold Vaughn's book "rifle accuracy facts".
To put that "slightly more dispersion" into its proper context, Case head internal diameter is about the same size of .284 Win, or the belted mag cases, but isn't anywhere near that of the .404 Jeffery derived short action and super mags, so assuming that everything else is equal, it won't shoot any worse than they do.
The marketing claim ( repeated by far too many gunzine writers) that a larger case diameter "is a proven bench rest principle/concept", is an egregious lie. The big reductions in bench rest group size accompanied reductions in case head diameter and backthrust, with the move to cases based on the .222 and the x39mm soviet (Mannlicher) head sizes.
I had a good chuckle at a 1960 s edition of Smith and Smith's " Small Arms of the world" which goes to great lengths to praise and brown nose any opinions of the united state military's top brass, and to disparage anything which seems to conflict with that prevailing received and nationalistically determined wisdom, which in that edition was that the .30-06 was the bestest possible military rifle round Evah... and as far as the 7.62x51 or anything else resembled the 06, it could probably be tolerated as second bestest.
The book lacks clear titles for which gun is being written about, but does have spurious "special note"s on almost every page. One, on the 7.62x39, says it appeared that the soviets were using the 7.62x54R anywhere that accuracy was required... The implication being that anything other than .30-06 (and when it came to pistols, .45 ACP) or that deviated in any way from them, just had to be inherently "inaccurate".
Those were the days before the .22 and 6mm PPC were developed on the x39mm case.
The later editions of "Small Arms of the World" that were edited by Ezell, are far clearer and more objective. The Ezells avoid the contradictions that inevitably follow from the Smiths' apparent use of similar criteria for truth and validity to those famously elaborated in the pronouncements of both the late united state Supreme Court Justice Oliver Wendell Holmes, and of soviet Comissar Lysenko.
Back to x54.5mm Swiss based wildcats. Happy experimenting!