I agree... the 'nail pattern' has nothing to do with the joists...
This is true although in a perfect world it should be across the joists as well.....
The joists most certainly run the shorter distance... which in your case is front of house to back of house, not left to right...
exactly 
As mentioned, grab a flashlight and stick your head in the hole and check it out.
In new construction or old construction that is in good condition, I think your 125 gal will be fine even though it is sitting parrallel to the floor joists... but since you keep saying that it is saturated beneath your house I would be concerned. Moving it against the front/outside wall will be safer...
that's what I was thinking also.Not so sure how strong it is but I cant see why it would be saturated either. If this is true, you need to get some french drains or something put in because this is not cool at all.It could lead to health problems and carpenter ants just love chewing on wet wood amongst other critters.
Although I would like to point out, if you own the house, moving your fish room to Room 3 would allow you to possibly tap into water/drain lines through the bathroom wall. Chances are the sink & toilet are on the wall shared by the kitchen, but you may be able to gain access at the tub/shower...
Not sure the OP is ready for that.If he hasn't gone in his crawlspace in 2 years since the house was bought...I don't for see him being into the renovation thing.(forgive me if I am wrong of course but it sounds like getting dirty isn't your cup of tea)
Cutting holes in your house to make fishkeeping easier is a definite sign of commitment... lol