I don't know much about rhubarb except that I like it. But I DO know about compost and mulching.
When mulching with compost, 2"-4" is preferred and use unfinished compost if you can get it. It's easy enough to make your own with deciduous tree leaves and lawn clippings ... just toss 'em together and keep moist. The taller (3'-4') the stack, the better for killing weed seeds, grubs and pathogens. If you have space to make additional piles, you don't even have to turn it. One pile "making", one pile cooking, one pile aging and one pile using. The exterior of the "using" pile becomes the interior of the "making" pile. Lather, rinse, repeat.
If applied heavily enough, compost all but eliminates weeding, encourages positive soil biota (which will basically keep the soil well-aerated and drained with no further effort from you), protects against rain compaction and supplies needed nutrients in-the-proper-proportions and on the slow-but-steady cycle living plants do best with. Every time it rains or you apply water, it weeps a "tea" of composty goodness that the soil microorganisms will make available to the plant as part of the symbiotic relationship.
If you can't make compost in a pile for one reason or the other, simply rake deciduous tree leaves onto the beds in the fall, watering generously as you pile them up. During the summer, use (no herbicides, please) lawn clippings to top off the mulch. In 1-3 years you soil will thank you with an abundance you've probably never seen before and the plants will be strong enough to withstand most stresses and more nutritious than anything you can grow with fertilizer out of a bag or bottle. Their roots will warm up slower in the spring (minimizing frost heave) and stay cooler during the dog days of summer and, because the soil loses less moisture at the surface and absorbs more moisture in the root zone, you'll need to provide a lot less supplemental water.
If you can still see the plant, you haven't over-mulched.
