FYI No biochar benefit for temperate zone crops, says new report

I am new to this and trying to be active. I have started a new field around a gas well, no soil test, because I had just picked up a disc. I planted wheat 9/26/16. I was thrilled that it came up nicely this spring with no inputs. This year, 6/8, again disced to incorporate the wheat, the ground was very hard, maybe compacted, dragged and planted sorghum, soybeans and buckwheat to keep the ground covered. I brought out garbage cans full of wood ash to spread. Had to throw it out by hand as I found out that my hand spreader could not do it. I know that I should have taken a soil sample to measure any changes, my fault. The ground is similar to the rest of my property, sandy and rocks. This will be my throw and mow or roll plot. I will take a soil sample for a baseline. I have read that wood ash has superior ability to raise PH. All of my other fields are low in PH and organic matter. I have added tons of pelletized lime per soil tests in other fields.
Any ideas on removing rocks, besides raking and removing by hand? Same request for wood ash as I would like more uniform coverage than just spreading by hand and following with a chain harrow.
Or am I overly concerned about rocks, I have already hit plenty with my brush hog clearing trails. I guess that I could mow higher or just roll with my cultipacker.
I am in Lewiston, Michigan, upper lower peninsula.
Thanks in advance.
I understand that this is where you would make a post about ash but from what I understand Biochar and just plain ash are two completely different things on a chemical level.

Biochar works like a sponge to hold onto soil nutrients and water so they dont leach away. They can actually hold and make the nutrients available for hundreds of years.

As far as raising ph goes ash will raise it much quicker so that the plants you plant soon after you apply ash will benefit from it but it will not last like lime does and you need to use a lot more of it. I guess if you have plenty of ash on hand my suggestion would be to add lime according to the soil test and also add ash so that the first year crop will grow better from the ash and the subsequent plantings will benefit for multiple years on the added lime. (lime takes three or four month to neutralize the soil)

Depending on what your ph is I would plant crops like winter cereal grains the first year for the reason that they can grow well on lower ph soils (5.5) than other crops. Add in some radishes for additional attraction and breaking up compaction.

If it is below 5.0 your best option I feel would be small burnett.

Do you have access to a cone style wheel driven atv broadcast spreader?

It might work well to mix the ash in with the lime. If the lime is damp and the ash is dry the ash should bind to the damp lime and help in spreading it so you don't look like a coal miner when your finished spreading it. If you don't want to add lime you could mix it with damp sand to help spread it. If the soil has a high clay content the sand will also help make the soil looser and clay soils take a lot more lime to neutralize than soil with a higher organic or sand content.
Thanks for the clarification. This fall in that field I will plant grains and maybe some clovers in that field. I have a drop spreader that I used to spread lime. It may have gotten wet because the agitators were bent as the lime solidified in the box. I have replacement agitators and will add the wood ash to the next lime application after a soil test.
Do you have a preference to mowing or rolling? I do have many large rocks in this field. My best field (another one) according to the soil test is rocky also. I have spent days removing football sized rocks. Working the ground has brought up even more rocks. Even though I have just acquired a disc, I would rather do throw and mow or roll, avoid disturbing the ground, build microbes and organic matter.