Are you sure your turtle is a female? Your description of a weird black lumpy mass reminds me of this pic:
viewtopic.php?f=14&t=30833If so, you won't have to worry about eggs.
Dwarf hair grass may be difficult to grow, even without a turtle to dig it up. Most aquarists who grow it use high light and CO2 injection. I'm not saying you can't grow it, but don't be disappointed if it's difficult. Anacharis is pretty easy to grow in a turtle tank, but your turtle will tear it apart and make a mess.
EDIT: That filter, even two of them, aren't going to be sufficient on a 100 gallon tank. You are going to want a large canister filter.
I can't speak to building your own filter, but I did build my own refugium. While I also have a canister, I suspect it would provide sufficient filtration. I'm not handy. It was a pain to build, but I grow plants in there to feed our turtle, as well as shrimp.
Basically, I have a hang over the back overflow. That drops water into a 55 gallon that is divided into three sections. The first is filled with more biomedia than three or four large canister filters. The next has sand, plants and shrimp. Then, there's a sponge like filter material separating the final chamber, which contains a pump for return.
I get to grow plants and shrimp for Tobi, where she won't eat them. Water changes are easier because all the new water is added at the third pump chamber. My overall water volume is higher, which means pollutants are diluted. My biomedia is rated in gallons.
Of course the big downside is an extended power outage when I'm not home (or the failure of the small pump on the overflow) means I risk breaking the siphon on the overflow. That would mean the pump would force water up and overflow the main tank, then start pumping dry and burn out.
I've been luck for a few years.
I'd suggest looking for craigslist deals that include a large canister with the tank.