1/8th of a tankful is a test load. You could also use one or two heavy people standing close together alongside the wall. And 12 sq. ft is a pretty big footprint, almost a distributed load. A crowded party would give you close to this kind of loading.
Depending on the calculations and the direction of the joists, the OP might get by just by doubling the joists in the area of the tank, over part of their lengths. For a 10' joist span, you're looking for a deflection of 1/4" or less, under full load. And you need the bridging at intervals to keep the joists from wanting to twist.
With the tank against the wall, the center of gravity for the tank would be ~1' from the wall. If the four tank supporting joists 16" OC are at right angles to the wall, there might be no measurable increase in deflection, even with a full tank. That's the best DIY solution; no modifications at all.
If the joists are parallel to the wall, you might need to double up only one joist. The tank would straddle the wall plate and the one joist, and the wall plate is not going anywhere. The one joist would see half the 1800#, spread out over 12'. For a full load test, get 5 guys and have them stand along the joist, one every 2' or so, and watch for a max. 1/4" deflection in the joist. This test might cost you a large pizza and some beer.