@SideshowBob why have I not been following this thread! Sub'd.
I don't think we've competed on Ebay yet, but we've definitely both been looking for the same Fiamme rims! Fiamme (and Mavic) licensed the Longhi patent in 1934 for 25 years -> 1959 (comments on the Fiamme timeline). So from ~ 1959 Fiamme would have been able to drop the "BREVETTO LONGHI", who knows if they were in a rush to do it. But that ties up with the timeline for version 2 -> 3 ~ 1959. Similarly the change in the oval decals mid 60s for version 3 -> 5, maybe that happened sooner, maybe they had a lot of stock of the "BREVETTO LONGHI" decals to run through :)
[I don't know about Mavic, their website says the patent was licensed until 1947 but that's an odd term and the decals have "Licence Longhi / Breveté France et étranger" through the 50s - e.g. the version with "MONTLHERY" written across the diamond I think is ~ 1960.]
As you say, it's hard to tell from the pics (similarly trying to figure out from Ebay sellers' pics) but are you sure yours are specifically 'track rims'? As far as I know the ones that don't take a brake are much more of a trapezium shape. The first ad attached is from Holdsworth Aids 1961, but there's very similar in the Ron Kitching 1955 catalogue. Other ads say the first pattern is good for 'road or track' and the trapezium shape is 'track only'. The conclusion I've got to is a lot of the period wheelsets on track bikes, or described as 'track wheels', had that first pattern and that causes confusion.
Anyway, long story short, I say if a brake block fits and is square to the rim then you're good :)
Regarding tubs: my view is if the bike is historically significant / you're hanging it on a wall then be as period correct as your heart desires. If you're hoping to ride around and have fun on it you don't want to be on 70 year old tyres, even if you can find them! So you'll end up finding 70s or 80s tubs that 'look period'. So why not just use modern tubs that look period :) Personally I like tan wall Veloflex - the Criterium are sick but a bit $$ (and admittedly a bit jazzy). I've also very happily used the more wallet friendly Vittoria Rally (the slightly older logo looks better than the jazzy current one) and you can get those in 25mm width (although I like the 23mm on the narrow sprints). I like the looks of the Challenge range but also $$ and I haven't tried them myself.
Personally I'd forgive non-period for any perishables like rubber, leather, cloth, so long as it looks in keeping. A few years ago when I was being more uptight about it, a wise man said "the air in the tyres isn't from the 50s" - Flash, Hetchins website.
If you're a member of the VCC try searching the library for 1947. There's a scan of 'Cycling Manual 1947' which is an interesting read. I've also leafed through the Cycling magazines - the ads give a good idea of what components were available / lusted after. I loved the article about Wally Summers in 'Cycling, Second Series, 1947 01 08 Jan' "One word provides the key to success on the continent. When mind and body revolt against the strain of hard riding, you must obey the call of Allez"!