(I've got to admit, this is one of my favorite arguments... it's like the cookiedough ice-cream of Wing Commander arguments -- so stop calling people morons, Earthworm, lets have an intelligent debate...).
Anyway, firstoff -- Wing Commander 1 ended on 2654.325... whatever date you get in-game is random, aside from the start (2654.110). The rest of the dates in WC1 can be calculated by in-game and WC1/2 guide references (yesterdays mission, earlier today and so forth) data from the official timelines and various other things (the date for the TCSO show, for instance, is given in Claw Marks). Here's the list...
2654.110 Enyo 1
2654.111 Enyo 2
2654.112 McAuliffe 1
2654.112 McAuliffe 2
2654.114 McAuliffe 3
2654.115 Gateway 1
2654.116 Gateway 2
2654.117 Gateway 3
2654.118 Gimile 1
2654.119 Gimile 2
2654.120 Gimile 3
2654.121 Brimstone 1
2654.122 Brimstone 2
2654.123 Brimstone 3
2654.124 Cheng Du 1
2654.125 Cheng Du 2
2654.126 Cheng Du 3
2654.136 Dakota 1
2654.137 Dakota 2
2654.138 Dakota 3
2654.139 Port Hedland 1
2654.140 Port Hedland 2
2654.141 Port Hedland 3
2654.142 Kurasawa 1
2654.143 Kurasawa 2
2654.144 Kurasawa 3
2654.145 Rostov 1
2654.146 Rostov 2
2654.147 Rostov 3
2654.287 Venice 1
2654.288 Venice 2
2654.318 Hubble's Star 1
2654.319 Hubble's Star 2
2654.320 Hubble's Star 3
2654.321 Hell's Kitchen 1
2654.322 Hell's Kitchen 2
2654.323 Hell's Kitchen 3
2654.324 Hell's Kitchen 4
2654.325 Venice 3
2654.325 Venice 4
Long story short there's a 'blank' period around the 2654 Sivar Ceremony -- when WCA takes place.
As for Tolwyn commanding the Tiger's Claw for a period -- this was established as far back as the Wing Commander 3 novel... Tolwyn accused Captain Thorn of incompetance, and took over command of the ship for himself. Tolwyn left before Thor's Hammer, leaving Halcyon in charge -- until Thorn was returned to us in SM2.
Another confusion regarding the Academy show is that it's set when they're *at* the Academy -- this isn't so... they're at a special command school, the Wing Commander Academy (check out the press kit which defines this -- we've got it here at the CIC!) after having graduated the TCSNA at Hilthros and passed through flight school at Sirius (what we see in the first episode).
Regarding the other ships -- Blair *doesn't* go through Wing Commander 1 flying just the 4 types simulated there... he flies the Epee, Ferret and Broadsword on WCA (and the old Rapier in the movie)! I don't think there's any canon reason why the Tiger's Claw wouldn't have other classes of fighters aboard her -- there's clearly squadrons that we don't fly out of in WC1 (some of them are even mentioned there!), so it makes sense that there are ships we don't fly (especially if you acknowledge any old-torpedo source, which would indicate that there is probably some sort of torpedo...).
Anyway, we *could* disregard the novels, movie, books and certain elements of the game -- but what would we gain? The concept of there being only four kinds of fighters in WC1? That's not much of a tradeoff, IMO.