The Room: 6'x9', Joists are 8" 16" o.c. Existing floor is 5/8" OSB + 1/4" plywood + linoelum.

The problem: Front Load Washer transmits vibration to whole house, as floor is not solid or level. This laundry room has to have a ROCK solid floor for this washer.

My solution: Remove Lino, glue and screw down 3/4" plywood (to subfloor- 1-1/4" screws and joists- 3" screws). Level floor with self-leveling compound. THEN lay down thinset and tiles.
Addn'l 2x8 headrs added between joists (maybe sister joists?)

Questions:
1. Is this a viable solution?
2. I've read there should be 1/8" gaps left between the added plywood (1/4" at the walls). Should something be put in the gaps before the self-leveling compound? otherwise won't that defeat the expansion gaps?)

Thanks for any advice!