the 5w-20 spec is for fuel economy. They undoubtedly tell you to change back after using 5w30 as a matter of being able to state their MPG numbers.
In my opinion, the engineers have specced the engine to be able to handle the load of the 1000 lb trailer while having 5w-20 in it for lubrication. Remember, the 5w-20 oils have different speccs to ensure that they stay in grade and dont thin out as easily when stressed.
So heres the issue... Go with a 0w-20 or 5w-20 oil that has the necessary specs for piece of mind, or go a little bit heavier, minus the specs, and hope that the viscosity provides reassurance. Tough call.
Buy do realize that ford truck engines are designed to tow heavy loads while running 5w-20... That may say something about the oils abilities, but not necessarily anything about your engine.
I would do one of three things:
1) run Mobil 1 0w-20... It meets all the specs, and is the right viscosity, but ought to hold up better in any situation, giving you security
2) run mobil 1 5w30 (or 0w-30, I suppose)...It does not meet the ford and honda specs for the lighter oils, but itll give you a bit more viscosity, while still being pretty close to what they spec your engine for. Remember, M1 30 weight oils are on the very low end of being 30 weight.
3) get a hold of the motorcraft GF-4 5w-20 and 5w30 oils. They are a group III blend, and are highly thought of on here. Keep 5w-20 in there normally, but when you change the oil prior to the season when you do your towing, maybe do a 50/50 mix of the GF-4 5w30. These oils are synthetic blends, should do well together, and the 5w30 ought to give you a bit more viscosity that youre apparently looking for. All while at least half-meeting the correct oil specs, and being quite cost-effective.
Id be more worried about your transmission and drivetrain than the engine. A 2.4L 4cyl engine can handle a pretty heavy load, its mainly reduced by the ability of the drivetrain and suspension to handle it. For example, the 138hp 2.4L 4cyl in my father's toyota previa is rated to tow 3500 lb. Its a RWD van though. My saab 2.0L turbo is specced for about 3000 lb towing, but it has a very stout drivetrain, albeit FWD.
Your engine may sound liek its straining, but thats more than likely due to gearing... a big 4cyl should be able to pull a 1000lb trailer without breaking a sweat, so long as you drive lightly and with good form.
Keep the transmission fluid changed often. I personally like to use OE or manufacturer tested and approved ATF when auto trans are concerned. Honda fluid is a good choice. Im sure there are good synthetics out there, but in an auto trans, I think fluid swapping is key, and I dont think that syn adds any benefits if things arent getting REALLY hot, since most of its properties which we love in engines are for naught in an auto trans, IMO.
Hope this helps,
JMH