The best I can tell is I am limited to 28 days a year. If the campgrounds have empty spots, is there a legal way to stay more than 28 days a year.
Simple answer: become a volunteer in some capacity. You might even get your fees waived.
For regular camping, it is hard to say. There's two primary reasons this kind of rule gets established (notice I did not say enforced, but then you are in an NPS area so don't be surprised if it is done in automaton fashion)....one is to prevent homesteading and essentially a semi-permanent presence, the other is to avoid any person capitalizing on facilities to the exclusion of other tourists.
With that in mind you may find that the reality is more lenient than written word (but you can't count on it without checking with the powers that be and even then you probably will get the 'official' version). Other land agencies typically have a similar rule that usually requires moving a certain number of miles after 14 days, more to prevent the 'living' on public land than any other reason. In those cases, a person could camp forever if they were willing to relocate every so often.
On the whole (personal opinion here) if a person keeps a clean camp, is not denying usage of facilities to others by their extended presence, pays their fees (

) and is not creating some problem by their presence it would seem of little consequence that they went over 28 days (other than the aforementioned zeal to enforce that the NPS likes).
After all, if you are in a 100 unit campground, when the relatively narrow high use periods are not occurring, and 10 sites are in use....what would the big deal be? A technical violation of the rule is all I could see being the case. Besides, they have a myriad (yea, a plethora) of other rules to lay on you if you are screwing up. It's not like you are hiding somewhere and they don't realize you are there. Since these kinds of rules are administrative in nature, in the real world outside the NPS, you will find officers using discretion in how or even whether to enforce the written word.
From a practical perspective, if you are separating your visits by 6 months, it's highly unlikely that they'd even notice (though now that you've indicated your interest you may be on the camper watch-list); it's doubtful they are that organized to track you. Maybe after a few cycles someone would notice you seem to be there a lot.