It sound like your pump is working too hard pushing fuel. this can result from kinked line, too restricted filters or if the pump is mounted too high in the system.
I would check the lines for restriction first. always use 3/8 in/out filter before the pump along with 3/8 hose like Fram G3 and replace it after 2-3 tank fill ups until your fuel tank is clean. A stock YJ/XJ fuel filter have a 3/8 inlet and 5/16 outlet is perfect as after pump filter.
If there is any sharp bending in your system using a hose replace it with hard line, when the hose get warm it become softer and collapsing, causing increased restriction. Never use fuel hose longer than 30 cm.
Remove the fuel lines away from heat source when possible or use insulation when not.
Make sure the return line is in good shape too and not smaller than 5/16 diameter.
As for the options you mentioned, the more flow flowing in the system the better, the extra fuel IS what cools the pump, with lower flow capability pump the problem will only worsen, assuming the current pump is fine. As for the inlet, 1/2 inlet will work better than 5/16, this allow easier "suction" resulting in less stress on the pump and faster priming.
I live in similar climate to Greece and with the right setup I have no problem even after 3 hours, mostly full throttle, of dunes riding at 45C.
A few pictures of your setup will help.
Thanks for coming back on this quickly. This problem has been plaguing me for a while now. Bear with me please for a few more questions, just to make sure I've understood this. From what I gather you are recommending that, unless I can get the pump in the tank, I should stick with the E2182 but make sure I set it up as you point out. So:
1 - If I can manage to put the E2182 in the tank, can I still use the stock 5/16 line that goes to the bottom of the tank to feed the pump, or will I need to replace it with a 1/2 inch or 3/8 line?
2 - Because it's more than likely that I'll have difficulties in puting the pump in the tank, I think I will have to get a 1/2 inch line from the lowest point in the tank to feed the pump. The pump inlet will be approximately level with this line and in roughly a straight line, but about half a metre from the point of fuel availability in the tank. To put a decent filter in between will increase this distance. Does this set-up sound OK?
3 - Because I may have difficulties in getting the correct size filters over here, can you let me know exactly which filter I can use pre-pump and after-pump so I can locate a supplier in the US and order them. One point here. Is it OK to use 5/16 outlet for the after-pump filter? At the moment the line from the pump to the fuel rail is 3/8.
I'll try to get a few pictures of the current set-up.
Again, thanks very much for your help.