I wouldn't use a particle blaster, regardless of the medium used.
There is too much chance of blasting to bare metal, ensuring future rust IMO.
If you're gonna paint, consider removing the vac canisters and everything else that prevents easy acess to the bay surfaces.
The absolute best treatment would be actual hot steam to melt the petrol/sand gunk and hi-pressure remove the assorted crud.
Perhaps there's a mobile steam cleaner in your area, or you could tow the rig to a shop with steam.
Lacking actual steam, I would do a multi-step liquid/scrub cleaning:
1. With plastic disposable putty knife, mechanically scrape off all built-up chunks of oil/mud/grease/dirt.
2. High pressure water blast (rental shop should have a decent one for about $25-40/day; blast your foundation or other neglected surfaces while you have it).
3. Apply a solution of Tide & TSP (actual Tri Sodium Phosphate, not 'TSP Substitute', you need the phosphates to dissolve petroleum products in addition to the detergents in the Tide); make sure you don't let this solution or runoff get into the waterways, as phosphates are really bad for fish and plants.
Scrub with assorted brushes.
Reapply the solution and allow to set.
4. Repeat high pressure water blast.
5. Finish with a foam engine cleaner that doesn't require a hot engine. This will remove the last vestiges of petroleum produts.
6. Rinse with water.
7. Getting the crud out of the seam spaces will be tough, might even require toothbrush work with SimpleGreen. But it's critical to removing contaminants prior to painting.
If there is ANY rust, mechanically scrape/wire brush all loose rust, then apply Naval Jelly to dissolve rust to bare steel.
Rinse, dry, and immediately apply a good rattle-can oil-based primer to prevent return of rust to the raw surfaces.
Protect the metal beneath the battery against future acid attack with a rubber coating like Herculiner.
IMO, an engine bay looks best in white, so one can better see sources of leaks. But, you have to keep it clean which is a PITA, especially if you do mud wheeling.
We don't do much mud in Phoenix.
Good luck.
-Rick