You are doing fine. However I suggest you only heat it to 185, just the 5 extra degrees can result in darkening of the syrup. Then test for density and adjust as needed, then grade it (color). When you fill your 15.5 gal barrels, they should be at or above 185F, then seal them. That way the syrup will keep for years if desired. If you can't keep up packing bulk, you may want to do it right after the season. The issue then is that you need to reheat it which gives a risk of making the syrup darker (every time you reheat it the syrup gets darker)
I do similar to how you are trying to go, but I heat all bulk syrup in my 2x6 propane fired finisher, then it is drawn off into my mixing tank (a 7 gal SS tank with bottom drain) then I add the filter aid, filter it and send it to either the bottler or if sending it to a barrel, I will have heated it to 200-205 so it comes from the filter press at 180 or more. When I do this I preheat the filter, to do that I heat to 200-205, filter and send it back into the finisher until the filter is hot. Then I start filling the barrel. In my case, my 2x6 finisher can hold well over 50 gal, and I'm filling 26.5 gal SS barrels. I have my draw off tank (off the evaporator) plumbed to the filter press, but I don't filter then, I just use the filter pump to move the syrup and I bypass the filter and send it to the finisher. It often takes a full 6 gal going thru the filter to heat it up (my filter is a Lapierre 7" with 5 sets of plates) When I have hated the filter I then make sure the syrup in the finisher is at or above 190, and I filter into a barrel, if I have enough syrup in the finisher, I fill a second barrel. I do not do partial barrels. If I'm going to do barrels I try to have 60+ gal in the finisher. I've never had enough to do 3 barrels in succession, but most often do 2. I suspect the producers you see filtering directly into barrels are big enough that they can keep the syrup hot enough, from draw off (219+/-) mix in filter aid, then filter with a still hot filter and into the barrel. It doesn't sound like you will be at that level yet.
Dave Klish, I recently bought a 2x6 wood fired evaporator from A&A Sheet Metal which I will be converting to oil fired
Now have solar, 2x6 finish pan, 5 bank 7x7 filter press, large water jacketed bottler, and tankless water heater.
Recently bought another Gingerich RO, this one was a 125, but a second membrane was added thus is a 250, like I had.
After running a 2x3, a 2x6, 3x8 tapping from 79 taps up to 1320 all woodfired, now I'm going to a 2x6 oil fired and a 200-425 taps.