Common rule of thumb w/ avg. fish load is 3x's the gph amount of filtration relative to the tank size i.e. 60 gal. should have ideally at least 180 gph of filtration so yes your 350 should be ok. When you start increasing your bioload/fish then it's best to also increase both bio & mech filtration & surface movement. Personally, if the fish can hang then I find a way to shoot for 5-7 times or more the gph filtered. Since I don't own a 350 & don't have a manual for it I don't know if the 350 gph is w/ or w/out media placed in it, sometimes manf. just show the best it will do for marketing, but when you read the specific's it can say something dif. when media is added. Redundancy = bckup safety, which is always a good thing.
I have used Hagen AquaClear pwrhd's for 20+ yr's. keep them maintained never a prob, unless run dry. For your 60 gal. I would use 2 AQ 50's adj. all the way open, w/ the air hose's attached to both, no real need to put the diffuser adaptor's on them just make the most of the surface movement. If you need to diffuse them a bit then you could point them toward the end's to so as not to blow the fish out of the tank, but the flow rate's are adj. on most all brand's these day's. I'm old school w/ an UGF on my 75 gal. & I run 4 uptube's w/ 2 AQ 70's on the end's pointed toward the end glass & 2 AQ 50's in the middle turned dwn a bit blowing straight out. Inexpensive prefilter's can be placed on the AQ pwrhd's if you're not running a UGF, which I think would have to reduce the flow even a bit more. If you choose to go this route, this of course would alleviate the need for you air pump or not that's your choice, I haven't owed an air pump since I started using pwrhd's. Don't remember the manf. but I recently saw a pwrhd on Drs.FosterSmith that said it could be run dry, which I would look into if I needed another, but I don't remember seeing a prefilter avail. for it. Hope this help's & wasn't tooooo confusing.