The best rates I see are with Solid Car Rental. However they do not mention rates for additional insurance. How much would that be? (LP mentions 15-25$ per day for basic insurance, are these figures still correct?)
Have you thought about just taking the taxi? They're not terribly expensive and there is no liability or headache. Usually I'll head to one or two places and just pay a taxi to get me between places.

dean's 4x4 rental has a mixed reputation. i know people who have used them to rent a cheap, used car and had no problems. others have had trouble. as long as you realize the risks of renting an older, used car.....
taking a taxi from place to place? are you serious? taxis are fine for local travel but to get around the country, probably the worst way to go. if you are going to pay that amount of money, you could fly or even hire a private driver who speaks english and can give you a running commentary and answer questions.

Renting an older car has it's risks no doubt, but not returning my calls for a few days when I had car trouble is unacceptable in my opinion and experience.

We rented a Suzuki Jimny which is (they tell us now!) not a 4x4, but still a SUV (jeep). Is that enough or should we try to change it for a 4-wheel drive?

as far as i know, suzuki jimmies are 4 wd. who did you reserve this with? what did they say about 4wd?

AutoEurope. We used this company in the past in Portugal, but we didn't know they also rent outside Europe (you have to admit, with such a company name ... ;-)).
Maybe they don't mention it as a 4WD because actually you can choose between 2 and 4WD with these cars. Anyway I'm pretty sure there is a 4 WD option, it says so on the Suzuki website.