What transmission do you have? If auto get a better trans cooler than the one it comes with. The engine can pull it, trans can handle it with a cooler and the frame can take a bit more than 1000 pounds. What you have to watch is braking and engine cooling. My tow vehicles are a '93 ford econobox with 63hp and 460,000km and a 2002 honda civic with 110hp. I towed a 5ftx5ftx8ft u-haul trailer weighing 900 pounds with each car on the same day. Civic got hot immediately and overheated just as i reached home just driving on the flat. Thats from wind resistance, not weight. The civic had new drums, rotors, pads and shoes but the old 63hp car stopped just as well as it or better, did not overheat and i went hours and hours with it up and down the biggest hills i could find. It also has almost as much towing power even though the civic has double the hp. I have had the civic 4 years and the ford 9.5 years, i do a lot of towing and prefer the ford.
The reason I said all that is to show that you need to try the accord first. It may do really well, or it may overheat. Change your brake fluid if you haven't and try it. Test the braking power on a deserted paved road and see what you think. Test it on a hill to see if it overheats.
Getting info from someone else who has towed with your exact car while maybe helpful may also not be useful at all. I towed this trailer:
900 pounds in the trailer and 500 plus me in the car. That was 5th gear floored on the flat but 4th on any slight incline (4k rpm but half throttle ish). The minute i took that plywood off it was like it wasnt there. You noticed it a little when speeding up and of course when braking but at 65mph i was using the same amount of throttle as every day going to work with an empty car. Its all wind resistance.
Also you want tires with good tread. If the tires on the accord are only so-so but new on the crv it may be cheaper on the extra fuel taking the crv than getting new tires on the accord before you really need to.
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