I agree with you in that acid adjustments, especially big ones, can best be made in two steps. That way you can see if you like the result as you go along. However, since you do have a pH meter, as well as a pH target, you can do a little bench trial first. Take, say, a 100 mL sample of wine from your fermenter (barrel, I assume) and add 1 g/L to it by measuring out 0.1 g tartaric acid on your gram scale. (As an aside — every home winemaker should own a 500 g x 0.01 g scale so you can measure little amounts of additives for bench trials.) Stir the acid into your 100 mL sample and measure the pH. Give it a taste. Do you like it? Do you want to add more? Since you’re starting at a pH of 3.9 and want to target around 3.6, depending on the buffering capacity of your wine, you’ll most likely end up adding around 2 g/L.
I would say you’re even better served just having a pH meter than the ability to titrate and measure TA. pH will give you a much better idea of the microbial stability (or instability) of your wine, meaning that bad spoilage bacteria love to live in a higher pH environment. By getting your pH down to around 3.65 or so (or even lower, if you still like the taste changes in your wine), you’ll lessen the chance of high VA (volatile acidity) later on due to growth of species like Acetobacter. TA is of less importance in being able to predict microbial stability in a wine. You can actually have wines with high TA’s and high pH’s some years; controlling pH is much more important for microbial stability so it’s great that you can measure that. But be careful with these wines, adding more TA in order to lower pH can raise TA to a point where it’s unpleasantly acidic. Tasting and testing will be key in these situations to strike a balance between the two.
I would say you’re even better served just having a pH meter than the ability to titrate and measure TA.
As far as how to add the acid so that it’ll dissolve and distribute well into your containers: Dissolve first, then distribute. Measure out the total grams of acid you’d like to add to your wine. Dissolve it completely in a small amount of wine, then distribute that wine back into your container by pouring and stirring well. For a barrel, you could even do a preliminary dissolve in a one-gallon (3.8-L) container, then add that to a 5-gallon (19-L) bucket of wine removed from the barrel, stir that and then carefully pour the 5-gallon (19-L) bucket back into the barrel. After stirring the barrel, it’s very likely the acid will be very well distributed into the wine.
It’s best to treat each storage vessel separately, as its own individual container. Let’s say you have a 59-gallon (225-L) barrel and a 5-gallon (19-L) topping keg and you wish to take each down to a pH of 3.60. Measure out the acid addition needed for the barrel, dissolve, and add it to the barrel. Then measure out the acid needed for the keg, dissolve it, and then add to the keg. If you measure out the acid needed for 59 + 5 (i.e. 64 gallons/242 L), then dissolve it into a small amount of wine, then try to distribute that liquid proportionately among the two containers, unless you do your concentration and volume math perfectly, you might risk adding differing concentrations of acid to each vessel.