1997 Mazda protege transmission, Hard shifting from 1st gear
I would try a flush. If its set up like my 96, and it likely is, changing the trasmission gasket and filter will be difficult. Mine has a medal plug on the bottom and takes an allen wrench, and possibly a breaker bar. If you take out this plug, drain, flush then refill via the dipstick tube and a funnel, it may help. You may need to do this a couple of times due to fluid still in the torque converter, pan, etc.
Lucas is good stuff, I would add it again when I was done. The tranny fluid should be pink, mine looked like used oil black before I flushed it.
Also, when adding the new fluid, shift slowly up and down through all of the gears to lube well and check your fluid levels after 100 miles or so, as sometimes a bubble will form and make it look full....then not after it pops.