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The 100 gal is going in a protruding bay window. It is centered over the concrete exterior wall and the support for the bay window looks pretty overbuilt to me - approx 10" centers with lots of blocking. The 200 gal doesn't have that kind of support though. It is going over the unfinished part of the basement so as you suggest, I'll shore it up from the bottom.
If the weight of that first tank is directly over the foundation wall, you should be good to go. If it protrudes out a bit, the area is probably cantilevered. It should be able to handle the weight but watch it's effects carefully. The other area could be supported by adding lolly columns in the basement below, which could support a girder.
Re: the parallel install. I will tell you, while it is in the NOFMA and NWFA manual to run the flooring at 90 degrees to the joists, I see it run parallel in some places and it appears to be fine. This is with 3/4" plywood ( not 5/8" ) over joists 16" oc. Your flooring contractor does have another option other than removing the wood and re-installing it. He could add blocking from below between the joists. This is a NOFMA and NWFA approved method. Simply cut standard 2 x 6 framing material into blocks that wedge firmly between the joist bays. Add construction adhesive to the tops. Pound them firmly up into place so the contact the subfloor and using a framing nailer and 3.5" framing nails, nail through the existing joists into the end butt of each block. Blocking can be offset to allow for nailing. NOFMA calls for blocking to be 16" oc. I think 20" should be fine but I'll concede to NOFMA's recommendation. I would strongly recommend this approach if at all possible. It would be a shame to tear out that flooring. Also, which direction is the most pleasing direction visually? Parallel to joists or perpendicular?