Best case is that you remove the boards and the existing insulation completely before doing air sealing--the loose FG has only marginal value, an inch of cellulose almost none. Ideally you are going to install 16-18" of insulation, so the boards will be buried and doing you no good anyway, in the long term.
Second best is to carefully move insulation aside so that you can still do a thorough job.
If there's a moisture issue, it's probably going to come from air leakage into the attic, not the presence of the boards, so the air sealing is critical.
Just adding cellulose insulation will not improve your air barrier. I would recommend removing the floor boards, spot air-sealing with foam (and rigid if necessary) at bypasses, etc. and installing new cellulose or FG. I would not recommend replacing the boards unless you plan on raising the platform to accommodate adequate insulation. I discourage attic storage --what's the R-value of a box of christmas ornaments or a suitcase crushing insulation near the platform?
Depending on the strength of the ceiling below and no can-lights, etc, you may be able to remove the existing insulation and dense-pack insulation below the boards from the ends or via drilled holes into or removal of certain boards. You may not achieve enough thickness and I would still be concerned with air and moisture migration since it's not a truly enclosed cavity.
If the air barrier is good at the ceiling below (obviously with no can-lights), you could just add more insulation on top of everything. Seal and bury the ducts as well. Avoid or replace your knob-n-tube wiring!
This seems to come up often, especially when customers want to keep the floor boards in place for storage. Best solution would be to remove floor boards, allowing for proper air sealing and achieve a minimum of R-38. Another option is to remove some boards to air seal, then inject dense pack cellulose. But, you will only get R-24. Not so great, and the utilities may not grant you an exception. Third option, inject foam into cavity (use injection foam and not spray foam). This will take care of air sealing, but again you only get R-30. Option 3 can also present some IAQ issues. If it comes into contact with any formaldehyde baring material, the formaldehyde will off-gas. Injection foam on a flat surface can also warp the material on which it sits.
So, remove the floor boards, do the job right and get rid of the old junk you are trying to store! IMHO.
Your last two statements, "The upfront cost of retrofits is a big barrier to comprehensive weatherization. Anything I can do to reduce the cost of installation will help," are compelling. You need a solution that makes sense, given the conditions.
I'd pull up every third or fourth board, as well as the perimeter boards, install baffles, and blow it to r-38 or r-49, infilling where there are voids in the existing fiberglass.
Even then, pulling the boards from anywhere but the perimeter may be superfluous. You could blow 16" on top and make sure the ends at the baffles are well-filled. And if the customer insists on retaining some floor space, build a dam around a section and call it good.
This may only be an 80% solution, but it may make the difference between an upgrade sold and efficiency gain lost.
We need to consider the extent to which some of our austere approaches to home performance scares off our customers, and sends the public a message that our field is unapolegetically fixed and inflexible. We don't have enough credibility among the masses to take that kind of approach. Yet.