rgrinder is correct about the dogleg transmission. If you get an L-series 5-speed dogleg (FS5W63A), you can swap an A-series 5-speed (FS5W63A) front case on it.

There is no 60L 5-speed for the L-series engine that I am aware of unfortunately so swaps have not been done.

Beware that the standard shift 5-speed (60A) is considerably different than the 4-speed.

You give me hope. I'm off to the junkyard to get an l-series transmission and see what I can do.
Thanks!

Actually, the differences between 4 and 5 speeds internally is behind the center plate where 5th gear was added. The front half (bell housing) differences have to do with which engine it bolts to, as in bolt pattern, etc.
A lot of the main shaft gears interchange between a given series of trans, it's the counter shaft (lay shaft) that's different because of 5th gear, but again this all lives behind the center plate.
Given this, IF you have an A series 60 series 4 speed, and an L series 60 series 5 speed, you should be able to put the bell housing from the A series in place of the L series bell housing and make an A series 5 speed out of it.
Don't quote me on this because there may be differences that I don't know about that could make this not work, BUT from what I remember from when I worked at a dealer it SHOULD work with few issues.

Not a chance

You can create an adapter plate or cut n shut the correct bellhousing. See Transmission Swaps

I've been looking for a '60 or '63 five-speed gearbox that'll fit an A-series engine. They seem to be going for about $1K. I can't afford that.
I can get a five-speed gearbox off an L-series engine for like $200, which I can almost afford.
I've looked at figuring out how to build a spacer that'd match the bolt circles to each other. Then the transmission's back the thickness of the spacer, meaning either I have to bodge the clutch bearing/fork forwards that thickness, or build a spacer that sets the flywheel back that thickness. That sounds easy! except then the starter doesn't contact the flywheel.
So what I'm wondering is: what does the inside of a 60-series four-speed look like? coz that's what I have, and I'm wondering if there's some magic by which I could put the guts of a 60-series five-speed, from an L-series transmission, into a 60-series four-speed A-series transmission case.
I'm betting the answer is not even a chance, it's totally different inside, but hey, maybe I'll get lucky.