I am by no means an expert, but I am playing a similar 4-3-3 with good results (once the team learned the tactic).
I personally would not use a DM set to BWM in this formation; I find them to be too aggressive (giving away free kicks/penalties and getting carded) as well as not holding position in front of the two center backs due to their high pressing level. This means that attackers can run directly at the the DCs and force them to close down the ball (leaving their position). I use either a DM (Def) or for my very best DM, a DLP (Sup) with one of the CMs set more defensive to provide more cover. I just find a less aggressive DM does a better job at shielding the Center backs. If you had extremely attacking FB/WBs (not that you do), even an Anchorman or Halfback would be a decent idea, as they stay even more centered and cover for DCs being dragged out wide due to your WBs being upfield.
Mezzalas don't defend all that much, especially on attacking duty. DLPs also don't defend all that much (relatively speaking). In my 4-3-3 I have at least one CM (Support) as a more general all rounder and often have two of them (depending on the particular CMs I'm playing that match). If I do go with one attacking CM that I don't expect to defend as much, their partner is going to more defensive (I do sometimes put a BWM at this position to cover for a Mezzala or other attacking duty if I have a good one).
I also would be hesitant to have two BPDs; they are both going to take more risks and potentially run a bit with the ball and get caught in possession. I have one CD I trust as a BPD and the others are standard DCs, to the point of not having a BPD if that one good one isn't in the game.
Another thing I always do that seems to help with solidity is set the AML/R to mark the corresponding DB/WB (so the AML marks the opponents DR, etc.) I do it by position, not individual player so that substitutions don't mess it up; make sure to check the opposing formation in-game and change the marking to WBL/WBR if they run DM-tier Wingbacks. They aren't usually great defenders or anything, but they do seem to come back more and somewhat track the opposing fullbacks. The downside is that you won't counter as effectively if they are pulled back into defense more, and (assuming they actually follow instructions and track back) they get more tired, so it's good to have subs for both outside attackers on the bench. But I prefer to win 1-0 vs winning 4-3 and it seems pretty easy to find decent outside AMs to allow rotation.
As far as the team instructions, it really depends on how you are conceding. I wouldn't usually have a high-press and prevent GK distribution set without using a higher defensive line as that causes your team to be more stretched out and makes pressing more difficult as your players are farther apart. Based on the recent match analysis, I would guess that their attackers are receiving the ball in front of your defense and playing through them on the break or taking long shots just outside the area due to the team being stretched and not being closed down effectively, but obviously would have to watch a game and adjust accordingly.
I actually tend to start with Balanced mentality with Standard-line/Low-Block and see how it goes, but that's more of an attacking style thing so there is no reason Positive can't be defensively sound. I also set Drop Off More as I find this helps with balls over the top and long through balls. Not completely, nothing will stop them 100%,but better. The flip side of this is that DCs are less likely to contest headers and balls to feet of opposing strikers, but I usually find that okay as long as it's not in the penalty box.
If my normal Standard line Low-block has them running at my defense, getting dangerous through balls in the middle or getting off uncontested longer shots, I'll flip to a more pressing style to see if I can disrupt them and get possession higher up the field (higher def line, high press, increased pressing triggers and Prevent Short GK Distribution).
And if that doesn't work and I just can't seem to stop them getting central through balls, I'll actually drop to a lower def-line/low-block, increase pressing triggers, turn off Drop Off More and set Encourage Crosses (assuming that crosses haven't been the problem). The idea is to remove the space behind the defense for through balls, but not to drop back into the box immediately; rather to create a hard stop line on the edge of the penalty box with the increased closing down and closer defensive spacing given by allowing crosses. Just making it harder to play through the defense. This is a last resort, clinging to a lead sort of strategy, but it has worked if they are bombing forward and running high tempo direct attacking. If they are patiently passing the ball around outside your penalty box, I wouldn't recommend this.
Also, don't forgot to turn off Counter-Press if necessary, especially when defending a lead, and even use Regroup. If you don't need to score late in a game, there is no reason to have players far upfield trying to press. Late in games I will switch off Counter and even go to Hold Position, slow down tempo, turn up time-wasting, set Be More Disciplined and even set Play for Set pieces. It's not exciting, but there is a satisfaction to watching the last 10 minutes of the game drain off without any highlights at all other than occasional free-kicks and corners.