I would till, but that won't stop the grass from returning. Blackberries should be able to compete with the grass. Not much that you can do with the ph at this point for long term change. I am not sure what ph blackberries prefer but changing it in ground is not generally possible without a great amount of expense.

Raspberries will do best long-term on raised soil, 6 inches or so. Perhaps you can get that soil from between the rows. Blackberries do fine on level ground and in damp soil.

5.7 pH is a little low. What is your average rainfall and is it concentrated in a rainy season?

Organic mulches will tend to pull the pH to neutral over time, and if enough, block the grass from getting sun, probably sufficient to keep the grass from growing vigorously and let your plants compete well (may not completely smother it though). Some sources say oak leaves may be a bit acidic to begin but tend to neutral eventually; probably acidic aspect minor if leaves shredded or partially composted. Add to the mulch periodically to keep the grass down.

Personally I'd avoid any landscape fabrics, eventually deteriorate and don't keep out the weeds, and then removign is a pain.

We average around 60" of rain each year in Bonifay, FL. The wetter season last 3 months, from June 5 to September 5. Least rain is Oct with around 3" and most rain is July with around 7".

Taking the dirt from in between the row is a good idea but I don't think I want the dirt/mud, I could put fabric down in the 5500 sq ft area but I think fabric in the long run is worst to deal with then just cutting the grass. I will consider digging dirt along my fence line to use in raising the beds as well as filling the divot in the blackberry rows after digging out the sod if I don't just till the sod in the beds.

If I pile up the oak leaf/grass mulch and wait a year could I use it as mulch around the blackberries and raspberries or do I need wood chips? I could buy a chipper since I have tons of pecan and oak branches, I don't think the Pecan Juglone is in the wood or bark but I'll have to look into that more.

If I buy Soil Doctor Pulverized Garden Lime from Lowes and work it in the soil will it hurt the bare root plant a month after applying the lime to the soil?

Raspberries will not grow well in FL. They cannot take the heat. I grew some a few years ago. If provided afternoon shade, they will last a couple of years before disease ends up killing them. My high temperatures never reached 100 degrees but they really suffered when temperatures reached 95 degrees.

The lime will not hurt the roots as long as it has time to react, really should only take a couple of days. The larger pieces of lime will continue to react slowly over time but not enough to burn anything. Ag lime is not caustic. Hydrated lime will burn vegetation but reacts quickly. The garden lime is probably Ag Lime (calcium carbonate and or Magnesium carbonate).

If it were mine I would till up 2 foot wide strips and rake out any grass, esp. Bermuda grass. You will not get all the Bermuda grass but with it tilled up it should be easy to pull out once it starts growing in spring. Any added compost or leaves can be added to the strips to help build it up to improve drainage.

Do you remember what kind Raspberry you had?

I seen a video when a man tilled the grass 1 time and then raked the grass chunks out and then continued tilling, then mulched over.

"Raspberries will not grow well in FL. They cannot take the heat."

I am not sure that is the case. Driscoll's, which is one of the largest producers of fresh berries for the retail grocery trade, has berry farms throughout Baja and Central Mexico.

Perhaps it is more case of high humidity rather than heat? At any rate, raspberries and blackberries are rather short term plantings anyway and should be replaced often (rasp - 2-3 years, blacks - 5-6 years) to maintain optimum productivity.

And as long as your soil pH tests above 5.5, both raspberries and blackberries should grow happily.

I had Anna and Heritage. They were both suppose to be more heat tolerant than other varieties. Dorman Red is suppose to be the most heat tolerant variety but people say the taste is very bland. Bababerry is one that reportedly grew well in south California. All the extension service publications I have seen from Gulf Coast states say that raspberries cannot take the heat. Blackberries are native to the area and will grow wild.

Here is a link from Mississippi extension service. https://msfruitextension.wordpress.com/2014/03/05/red-raspberries-in-the-south/

All the other southern publications I have read comes to the same conclusion, really not worth growing in the deep south.

The agriculturalist form the county also told me raspberries won't grow due to not reaching chill hours and the humidity. I figure what the heck I would try 2 plants of each and see what happens, I love raspberries and if I fail I will know that I at least tried, i'm in zone 8b - 600 chill hours.

I had Dorman Red in Atlanta, GA and I actually like them but others didn't.

Never hear about the chill hours on raspberries. I am in 9a and they bloomed and set fruit. I have always heard Dorman Red will grow down here. I think they would be your best chance. I would still try to give them afternoon shade if possible. Grow them on the west side of house or wooden fence.

Some of the blackberries do have chill hour requirements. Other blackberries are fine with only 100 hours of chill.

With 60" of rain, the raspberries will do better long-term in raised ground.