Yes that's a decent idea. Off the cuff thoughts:
Canadian F.3s as a replacement for the Voodoos. Maybe they bought F-16s instead of F-18s to replace the F-104s & F-5s, but then needed something heavier for the domestic air-defence role. Note that Canada was in the MRCA programme at the start.
Australian GR.1s to fulfil the F-111 role after the latter was cancelled back in the 1960s. Maybe the Aussie ones would be hybrids with F.3 fuselages and Hindenburger tanks but GR.1 radomes/avionics to get the maximum range strike platform.
Other middle-eastern export customers apart from Saudi Arabia. Oman, Kuwait and Jordan would seem possibles. Oman actually decided to buy Tornados at one point but then cancelled.
Dutch GR.1s. The Netherlands was also in MRCA in the early days.
Dutch/Belgian/Danish/Norwegian GR.1s. Maybe the Starfighter/F-16 nations elected to buy fewer F-16s in the '70s and wait for the Tornado to fulfil their strike requirements?
JASDF Tornados. Japan considered the Tornado IRL before opting for the Mitsubishi F-2.
Spanish Tornados. What if Spain had joined Panavia in the way they later joined Eurofighter?
Taiwan and South Korean ECRs: both showed an interest in real life.
More traditional recce version than the real GR.1A, with the main radar removed (I think they'd keep the TFR) and a nose full of cameras. The F.3 radome might be a suitable base for this, rescribed with a smaller TFR radome at it's tip, windows cut in the side and a canoe fairing for a front-facing one.
French GR.1s

. Bought instead of Mirage 2000Ns as a trade-off for the Panavia nations buying Mirage 2000s/4000s as fighters to replace the F-4Ms, F-4F and F-104S.
South African GR.1s, bought to replace their Buccaneers in a timeline where there was no arms embargo.
Indian GR.1s, built under licence as a follow-on program to the Jaguar.
Comedy build #1: 1/48th fin on a 1/72nd fuselage, or 1/72nd fin on a 1/144th fuselage to honor the 'Fin' nickname.
Comedy build #2: take the spare fin from #1 and put it in a sea diorama, sticking straight up out of the water and heading for a swimmer in Jaws fashion.