I used to shoot a lot with my 11-87 special purpose for doves. When you say cycle "well" I assume you mean without fail. I never had any issue with the high velocity 3-1/4+ dram types or the 1-1/8 oz loads. If you're reloading I think you want the higher pressure type, i.e. 9000 psi+.
I have shot "hunting" loads in the 11-87SP with no hiccups. I've shot reloaded target loads of 1 oz. or 1 1/8 oz. with no problems as well. Factory 1 oz. @ 3 1/4 dram loads work fine as well.
Loads in the 6000psi-7000psi range may not fare so well. These same loads won't completely cycle my Browning 2000 either. I would stick with the advice given and look for reloads in the 9000psi range or factory skeet fodder, preferably 1 1/8oz.