Can I add insulation to my attic and put down plywood so I can walk around more easily?

Lay rigid insulation boards on the joists and top them with plywood.

The compressive strength of the insulation boards will be plenty for storing whatever you can carry up there. The load will be spread across the joists. It's unlikely that your ceiling will collapse under the weight of a few boxes but if you're planning to put anything heavy up there, you do need to consider the construction of the building in more detail.

Rigid insulation boards will insulate about four times better than the same thickness of fiberglass insulation which means you can use 2 or 3" thick boards. Lookup R-values if you're interested.

1. Remove enough of the existing insulation to expose the top of the ceiling joists.
2. Put down rigid foam boards on top of the joists (I'm familiar with Kingspan and Celotex in the UK).
3. Tape the boards with foil tape to keep them together and stop draughts.
4. Top the insulation boards with plywood or chipboard.
5. Screw the plywood sheets together with short strips of wood to avoid them slipping apart from each other and leaving gaps or find some way of pinning them in place around the edges. (I didn't do this at home and they've shifted a bit).
6. Use the fiberglass insulation that you removed to top up the insulation in the rest of the attic (where you didn't lay the rigid boards).

I've done this in our house in the central part of our attic. The problem we had was getting the boards (insulation and chipboard) through the small hatch but yours may be different. For the chipboard, I bought narrow tongue-and-groove "loft boards" designed for this purpose but for the insulation I had to slice it in half on one side and snap it back on itself to be able to get it into place; then I taped it back together.

I haven't yet needed to get to any of the electrics underneath. Some of the wires were rerouted around the edge and the bathroom fan is away under the eaves with hardly any headroom so still accessible under the mineral wool insulation.

Here is what I am going to do -

1. Add insulation in the attic. Most likely remove the current mess and add new R-49 faced fiberglass.
2. Make a few upside down Y saddles with 2X6s to support some plywood for storage flooring.
3. Cut a board or two to leave in the attic as portable working surfaces so I have a place to either sit or kneel as needed.

I appreciate all of the assistance, and sorry for the discussion aspect of it. I would have used the foam board but the highest R value I can find is R10.