Deck for new tub

[wvance]

I'm having a Hot Springs Flair delivered in about a month and I need to build a free standing platform for the tub to rest on.  According to the tub's literature I need to plan for a total load of 120lbs/sqft evenly distributed across the 49 sqft.  This includes live and dead load, of tub, water, 6 occupants @175 lbs each and building materials. My plan is to build a 7x7 platform 15" above grade, supported by 3 beams, one on each end and another at the center line.  Each beam would be supported by 3 notched and through bolted 6x6 posts. For the beams I was going to double up 2x8s glued and screwed.  Joists were going to be 2x8s,  12" OC, hung on Simpson hangers. Each face of the platform will be X braced.

I know I wouldn't need the center beam if I increased the size of both beams, and joists but due to my good old Ohio clay my footers would have to be pretty big to distribute the load and would have to be hand dug.  With the 3 beams I can use an available auger for all but the center post.  Also using the 3 beams allows me to us smaller boards and allows more airflow under the platform due to it being so low to the ground.

So can someone tell me if my math on all of this is right? All of this is assuming Southern Yellow Pine.

Center beam carries half the load. =.5*5880lbs=2940 lbs

That load over the 7 total feet is 420 lbs per foot. This is only 44% of the allowable 958 lbs for double 2x8s over a 4 foot span. (My span is only 3.5 ft)  The outside beams are going to carry half of the load on the interior beam and would only be 22% loaded to max.

For the interior joists the total load area over the length of a joist would be 3.5 sqft (joist span of 3.5 ft at 12" OC) which is 120 lbs per foot.  This is only 25% of the max load of a single 2x8 (479 lbs).  The rim joists would be half the load again and would be fine at 12.5% loaded.

Joist hangers would carry half the load of each joist .5*120lbs*3.5ft=210lbs  Appropriate Simpson hangers using their fasteners hold anywhere for 700-835 lbs.

I believe the entire platform could be build on 4x4 posts but I'll be building out of 6x6 so I can notch them. The very center post will carry 1470 lbs, so I'll have to pour a 1sqft footer to carry the load due to my clay's holding ability at 1500-2000 lbs/sqft.  The other posts will carry either 735 or 368 lbs depending on location so those footers can be sized appropriately smaller.

What am I missing, other than the obvious stamp and education of a structural engineer?