Isn't the real issue here just that you mixed way too wet in the first place, not the heat itself? I've laid plenty of block in Phoenix summers and a wet mix has always been the wrong move no matter the temp, because water is what kills the bond and makes the joints shrink. You said yourself the stiff mix worked fine once you stopped adding water, so it sounds like the heat was never the problem you were fighting. Waiting 10 minutes to let it set up is good advice, but that just means your mix was right, a wet batch would still slump and crack even if you waited. If you want more working time, mix smaller batches and keep the mud in the shade instead of drowning it. Adding stuff to slow it down is mostly a band aid for a mix that's too loose to begin with.

Did you check the gear oil yourself before buying it, or just take the seller's word? Those towable units run hot and if nobody ever topped off the gearbox, the bearings are already toast by the time you get it. Pull the drain plug and look for metal shavings, that tells you right away if it's worth fixing. On a $600 unit the rebuild kit plus labor usually runs close to what you paid, so unless you can do the work yourself, it's often better to walk away.