Your plan isn't a bad one, but I hope you'll think about a couple of things:

I don't really know if the bricks would work, unless you mortar them together. The only barrier I've ever had that has done a pretty good job of keeping bermuda out was the green steel edging that you hammer into the ground. That worked pretty well for us in Fort Worth in black clay soil in the back yard. If the bricks aren't mortared together, I think the evil bermuda stolons will creep in between the bricks.

One reason raised beds work so well is that your feet stay on the pathways (I hope) and are not walking on the raised beds compacting the soil. If you convert to one large raised bed, you're more likely to walk on the soil in which the plants are growing and that will cause soil compaction. Soil compaction can affect how well the plant roots grow, how well the water soaks in, etc. Remember that plant roots technically do not grow in the soil, they grow in the air pockets between particles of soil. That is why clay soil is so hard on plants....the particles stick together and it is hard for the roots to find air pockets in which to grow. I used clay as an example because it compacts the worst, but even sandy loam can become pretty compacted if it is walked on regularly. So, if you want one large bed, think about what you might do to avoid compacting the soil.

Mulch is important too, not just in pathways but in the raised beds as well, regardless of their size. Several inches of mulch keeps the soil more cool (easily 20 degrees cooler in hot summer weather) which improves plant growth and productivity. Mulch also helps keep weeds down and makes the weeds you do have (including invading bermuda grass) easier to remove because they are growing in mulch and not as much in the soil. Mulch reduces soil splash when rain falls and this is important because rainfall can splash soilborne diseases up onto plant foliage. Mulch also helps reduce both wind and water erosion. Mulch also helps soil hold moisture and reduces how often you have to irrigate. Personally, I wouldn't attempt to garden without mulch.

There are all kinds of mulch--not just wood chips. I use a lot of straw, some hay, tons of grass clippings from mowing our yard, and all the chopped/shredded leaves I can round up in the fall and winter months.

Another very important fact about mulch.....as it decomposes, it enriches the soil. You really don't have to add any amendments to your soil over the years as long as you mulch. The mulch decomposes and turns into humus or compost and enriches the soil. The decomposing mulch attracts earthworms and they help carry the compost down into the soil, further enriching it. So, mulch is one of the most useful garden helpers around, but it doesn't have to be expensive purchased-by-the-bag wood mulch.

Also, be very careful with the siting of your trellis. You want to place it in a manner that it will not excessively shade the rest of your garden and interfere with proper plant growth.