Since you mentioned cheap, then logs from your land are about as good as anything else. I'd use Oak or a hardwood if I had them. Probably use four of them as over kill and put two side by side where the tires will put all the weight. I'd also cut them so you had allot of overhang on either side. At least ten feet. With a 12 foot span, I'd want the logs 32 feet long.
Then I'd deck them with PT 2x6's or bigger. I've never done the math, but I'd check to see what the price is per square inch of PT 2x8's, 10's and 12's.
The problem with the trailers and other metal existing contraptions is the amount of fabrication that will have to be done. As soon as you start removing material from it, you loose allot of strength. The only trailer you should consider is a flatbed. Finding one will be a challenge because so many people are looking for them. It could easily cost many thousands of dollars for a used, beat up one.
How steep are the banks? Pouring concrete across the bottom and letting the water run over it is a very common method for crossing creeks. If the water it too high, you can't cross it, but if it's just a few inches, you can still drive through it on top of the concrete.
Eddie