[PureHarvest]

First thought: you can not physically remove bermuda grass from digging and tilling. You most likely just root pruned it and it will branch from every point you broke it off and it will still continue its spread to take over the world. There are so many stolons and rhizomes that are still in the soil that will take off next year. It is unreal.
I would spray an area 2x the size I want to grow in if it was bermuda. Probably too late now as it is dormant most likely. Spring dormancy break and late summer before entering dormancy is the time to spray.

Your soil. You can not not change the texture of your soil. You can change the structure and % organic matter. By all means add organic matter and do cover cropping. Do not till it in (mixes up the structure). Keep adding layers to the surface, and move the material aside as you plant, then scoot it back.
Leaves or grass or hay layered over the garden will smother weeds and maintain the top layer (A horizon) which is where your organic matter is located in which makes the topsoil or plow layer. It will also help the sandy soil retain moisture.
If you do a cover crop in fall, come spring, do not till it in. Mow it down 2-3 weeks before planting and leave the clippings on to keep weeds from coming up.
You already have topsoil, mixing organic materials into the soil is a waste of your energy. Layer it on top. Look at a natural prairie or forest. Things are never mixed. Layers are added on top and the soil is always covered. Roots grow down and die off or slough off layers. Crowns die, blades die and layer on top. Worms find this area the most desirable. Things are not all mixed up and the soil rhizosphere is able to become complex when it is not tilled and the organic matter then oxidized.
Then you just need to come along and supply some ingredients to supply the needed nutrients for the crop. You can do the organic route or CORRECTLY supply the PRECISE amounts of soluble ferts at the right time in the right forms and not "kill" your soil or the world. That's your call.

Organic route as far as N needs: Alfalfa pellets at 5% Nitrogen:
Tomatoes in a sandy soil will need 120 lbs per acre of nitrogen per year added. You have 500 sqft. That is .01 acre. .01 x 120lbs = 1.2 lbs of N for your garden. 1.2/.05 (5% N in alfalfa) =24 lbs of alfalfa pellets for all your N needs for your 500 sqft garden. It will not be available right off the bat, so needs to be added well ahead of planting, or soluble fert needed at plant out. Of course that does not address the K that you will need nor other nutrients. My loamy sand also needs 150 lbs/ac of K added every year, and I keep an eye on Cal and Mag along with micros. Just had a test done last month. Last one was done 2014. Still needs K. The pH and Cal, P, Copper, Boron, and Mag are unchanged in 2 years.
Alfalfa pellets will not "build" your soil, just add nutrients. Plant roots via cover crops, not tilling, and leaving a cover of plant material on the surface (in that order) are the top things you can do to improve your soil health. People underestimate the value of living and dying roots year round from fall and summer cover crops and your main crops. Much more contribution there than what is above ground, especially if you use a mixture such as Rye/Radish/Clover. Use a dwarf clover or go with an annual plant in your walkways in summer. Smother the walkways in the fall with leaves/clippings and plant into the walkways in the spring. No spraying needed. Tilling anywhere along the way defeats a lot of these efforts.
HEAR ME tillers, not saying your method doesn't work or you're a bad gardener. This is what I would do in my loamy sand (but also did with my clay back in the day and never had to use a tiller). Let the biology do the job for you.