There are some very good points here in some knowledgeable answers/counter questions.
I find it difficult to add to some of these types of questions, owing to the fishing here being very different from the fishing there (in most instances).
Personally, if "down & across" fishing here, I am on fairly large rivers with good flow and rather cunning wild brown trout. Most times if I have to think "was that a take?" I am too late and have missed the fish, they are that subtle. Brown trout will sip in a fly and spit it out with very little "feel" relation back to the rod hand here.
So my usual method will be a fairly tight line compared to what most of you will be used to. Initial cast is often 30 degrees rather than the traditional 45 degrees, sometimes I will curve the leader upstream to give the flies time to sink before they are really "fishing" on the end of the straightened line. Mends come into play early on, as soon as the line lands- generally, but there can be small mends on the drift. Rod tip is pretty low, almost on the water, so the line is in a straight line from the stripper guide to the flies (in theory), thus eliminating slack line as much as possible. The line is "held" in my off hand by looping over my pointer finger and trapped by my middle finger, approximately 8-10" from the stripper, but tight between the two. There is slack line behind the off hand and reel.
I rely heavily on felt transmission back to both the off hand through the line and grip hand through the rod (glass rods are so much better for this). Now usually, lifting the rod tip is sufficient to set the hook- if you do not move the off hand from its position and there is no slack in the system in front of said hand. Similar to lifting the line to back cast- eliminate slack and lift the rod.....
If the take fails to hook up I will often feed a short length of line with my off hand so the flies settle- often this will induce a second hit from trout as they think they wounded the food initially- if they were not pricked by the hook point!
Really hard to say where things might be going astray for you without being at your side and I can tell you how I do it until I am blue in the face.... but it might not work where you are.
One thing you might want to try is using an indicator. It kind of makes you concentrate on the wrong thing ideally, you watch the indicator instead of feeling the fly/flies, but they can be a huge help also. If for whatever reason there is slack in the system, your line is drifting in front of your flies and you have lost touch with them, an indicator can be your friend. If a floating indicator stops, changed direction, dips, or just does something other than float down at current speed- strip slack line in and lift the rod tip- odds are you will be hooked in.
Timing of the strike? I believe this has a lot to do with local conditions and type of fish you are targeting. Brown trout differ from Rainbows and I dare say Brook or Cutthroat differ again (we do not have those). Wee trout tend to be quicker than big trout...... there are lots of variables. Big one I discovered is that Northern Hemisphere trout seem to be a lot quicker than their Southern cousins- you have to be pretty smart on those. But here, I tend not to give any spare line before lifting into a take when down & across fishing. My reaction time and the time it takes for the line to lift as I feel the initial hit seems to be the ideal delay.
From watching trout feed here, often they will turn slightly as soon as they take naturals sub surface and dart back to their lie, so that kind of leads to them hooking themselves. Honestly, the timing thing- you have to decide that for yourself on the water in my opinion.