I also have seen a similar problem due to debris (mostly rust) clogging the metal filter of the reg (not the dip pipe). The interesting point is that when this happens, the SPG still indicates the true pressure in the tank, as the minimal air passage remained is enough for pressurizing the SPG. But when you inhale, then the indicated pressure drops, and then comes up again slowly...
A freshly replaced filter on the reg could help, but just partially. So when this occur you still have problems using your own reg (as it happened to me).
Here in Italy all tanks have two valves, and when I was trained the rule was to always mount two independent regs, with two first stages. This can make a case like yours not so dangerous, although the secondary reg usually does not have any SPG, nor the hose for inflating the BCD; so a failure of the main first stage is still a severe problem.
But there is little else you can do, as the tank is almost inevitably rented when you fly to a remote tropical place.
Now that the standard here is to use DIN regs, which are much safer, most people (me included) is not using anymore two independent first stages.
So you can just hope there is not too much debris inside your rented tank.