With a bad shoulder you dont wanna try this, take it to a dealer or someone
you can trust.

Did you try to back wash it Tim?  If you have to replace it, you'll probably
want to take it to a garage or a friend if your shoulder won't allow you to
bend into impossible positions.

Can tell you about a 94 Blazer S-10 version.

The GM service manual says to entirely remove the instrument panel.  I found
a way to do this without removing the electrical cabling etc at the drivers
side in order to access the heater core.  Everything else does have to go.
This gave me enough free rein to pull the instrument panel out on the
passenger side and move up and down to facilitate replacement of the heater
core.

Got the heater core out yesterday afternoon.  Found that the replacement was
too deep and wide to fit.  Gave Autozone a call, they said the one they sold
me was for a S-10, not a Blazer S-10.  Don't think you'll run into that
problem though.

Didn't find anything terribly awkward for accessing screws for removal.
Some of the electrical connections are not very intuitive, be careful not to
break these.  It is a big job though.  Take some digital pictures for screw
replacement etc along the way.  Don't forget the air ducting and ECM module.
Disconnect the negative side of the battery before starting.  On the Blazer,
the screws that hold the heater core bracket are 1/4" socket type, if the
same on the Jimmy, you'll need a 1/4" socket with a 1/4" driver and a 1/4"
extension.  A 3/8" to 1/4" adapter at the socket won't work as it gets stuck
between the panel and the heater core.
............
Jonny