Although you may be "OK", if it was my house, I would (and have) put additional support for peace of mind. When it comes to this stuff overkill isn't really a bad thing, IMO, so you done right by at least considering. What you have going for you is that the location is running across the 5 beams. I would still sister the boards and/or have additonal posts or jack support. Depending on your type of stand, that could add a couple hundred lbs too.
My tank/stand (~ 3500 lbs) it is sitting parallel to the support beams, but also exactly above a 20+ foot long 4x8 beam running perpendicular held by 4x4 posts (I have a crawl space, no basement). So I ended up putting two more 8 foot, 4 x 8 beams running parallel to the existing beam (all held up with 4x4 posts as well).
BTW, will having the tank by the window be a concern for you? I think it will look nice in your office though.
My tank/stand (~ 3500 lbs) it is sitting parallel to the support beams, but also exactly above a 20+ foot long 4x8 beam running perpendicular held by 4x4 posts (I have a crawl space, no basement). So I ended up putting two more 8 foot, 4 x 8 beams running parallel to the existing beam (all held up with 4x4 posts as well).
BTW, will having the tank by the window be a concern for you? I think it will look nice in your office though.