I agree the best method is keep at it, IF the tank drains you are in luck If the tank does not drain, I have a suggestion but I'll hold it for a bit.
Keep using Washing soda or Dawn Dishwashing liquid (NOT the Anti-bacterial) Add a biological agent to the tank to encourage cleaning
Tank rinsers come in a few different designs
My rig came with a tank rinser called "The Flusher" Far as I'm concerned that unit belongs in the black tank cause it was a piece of... What goes in the black tank. I replaced it with "The Tornado" a much nicer unit, but you are no where near ready for that upgrade yet, that comes AFTER you clean the tank
So long as the tank drains there are two kinds of rinse wants... I have one and kind of made a version of the other
The one I bought I wish I had not, it is a flexable hose with pin size "jets" at the bottom, not really very good at all
The one I wish I bought is called "The Twister" this one has a brass "Spinner" on the end with angled jets to spin it. This one stands a decent chance of actually WORKING
The one I made, which for you might be the best, is constructed as follows
About five or six feet of 1/2 inch PVC, a pipe cap and a hose fitting (I used male and use a double female adapter to feed it)
In the side of the cap, in line with the blue line on the pipe, or the printed line on the pipe (pick a line) I drilled a hole, My hole is about 7/32" as.. Well.. That's the drill I grabbed first, exact sice does is not critical but between 1/8 and 1/4 is suggested
I use a combination feed considting of a valve feeding a SPRING check valve feeding a Brass Vacuum breaker feeding the double female hose which feeds the washer (Takes longer to type this thand to put it together)
Now I have a JET I can aim to where it will do the most good. I can hold it and slowly move it and a jet that powerful (City water is around 80psi) will chew through solid rock if you hold it long enough (i'm not kidding here)
I would use such a wand, and then use the assorted "GEO" methods, and then when parked fill the tank about 1/2 and add biologicals (Ordo-los or Power or any of the enzime/bacteria products, Even common yeast will help)
Rid-ex if you plan on letting it sit for months
Lots of things, all eco friendly.
And if all else fails I'm told there are companies that pressure wash those tanks Somehow.. NOt a job I'd want.