Sounds like you're doing everything right! Yes pine straw for the strawberries! Once it settles in it stays. Usually you don't want to fertilize these in the spring. Once they flower and start producing is the time. Check out strawberry.org. It has good info on feeding. Do you have everbearing or summer bearing? With summer bearing you feed after they fruit. You start feeding everbearing anytime, as they keep producing. Better info at site mentioned. I have both. I need to check the site too.
I put compost down for my raspberries and blackberries in the spring. I guess late fall would be ok too. I mix organic fertilizer with the compost in the spring. Also any amendments for trace minerals, like azomite, or green sand. As minerals should be added too. I rotate usually, green sand one year, azomite the next. Kelp also provides trace minerals. Rock phosphate , lava sand or other mineral sources can be used also.

With pine straw you can add compost right on top and put a fresh layer on. But I remove most, and with wood chips, yes slide them to the side add compost and put them back.
You really do not want mulch in the soil as they require nitrogen to breakdown and may rob the plant of needed food. You can add extra nitrogen to remedy too. Apparently on the surface it not a big deal. Not sure I get that? But that is the general consensus.

For raspberries and blackberries I add more organics in July, and once a month hit them with a soluble fertilizer also. They need a lot as canes are forming all year, and flowers and fruit. I may hit them Sept 1st for the last time, as fall bearing are producing.

I am having a lot of trouble with pine bark mulch in my strawberries.
They all develop fungus on the berries. Did not have that trouble
last year as I did not use pinebark. Not sure if pinebark is the only reason,
but be Leary?

I was able to round up pine needles from our property to mulch the strawberry bed and I'm hoping I can do the same with the raspberry and blackberry bed. I think I will easily be able to remove them and put them right back when I want to add amendments to the soil.

Drew, do you use any fish emulsion? Beyond compost that's all I've used before for fertilizer. But, I really don't know how much to add. I've read everywhere that it can be used, but can't seem to find direction on the amount.

Pharma, I don't have any experience with mulching around strawberries since this is our first year, but I have heard that pine needles are great for strawberries. If you don't have pine trees to pick them up from, my local nursery had pine needle bales for around $6 each. I'd never seen them sold elsewhere before, but some specialized places might offer them.

One nursery/grower lays down straw around the plants.They say among other things,it keeps the berries clean from splashing when raining. Brady