Ill be committed to an asylum for this BUT I don't actually think anything drastic needs to happen..
Bring in another CB
We need to bring in another hard-nosed, "stick my head on everything" CB. Shawcross, Dann, Smalling...maybe not those players themselves but that
type of player. So we would have Jagielka or Shawcross, for example, partnered with Stones or Funes Mori.
Medium block or press
I am not teaching anyone here anything they didnt already know, but let me say it anyway.
There are 2 choices seemingly under Martinez for how we defend when we arent in possession. We either press high (FA Cup, vs Chelsea) or the more routine 'medium block' i.e. let the opponents have the ball until they enter our half. Once they do, each player attacks 'his man' or alternatively attacks whoever has entered 'his' zone i.e. if a defender looks to bring the ball out.
He uses this so that a) only the usually redundant (in an attacking sense) defenders of the opponent have the ball in a relaxed state (i.e. players that cant hurt us) and b) allows us to draw out the opponent and counter-attack.
For me either work fine
as long as the entire team do it. Against Utd, for example, Lennon pressed high as did McCarthy sometimes, but everyone else kept shape and in-line with the medium block strategy. Make no mistake, for all my defences of our manager, having a team who does a bit of everything is NOT acceptable. If we have a set, disciplined game plan - and it can vary game to game - then we will see alot of the pressure taken off the defenders.
Practice and perfect defending set pieces/long balls into the box
Because we are so disorganised (see above) it means the defence are under alot of pressure. This causes mistakes, both individually and collectively. Together with some practice (doesnt have to be laboured training Roberto!) and perfecting our defensive shape, it will mean that our defenders are in a better place - both in condition and in practice - to defend against the long ball.
Stay injury free
I do like the OP
@Zatara but I disagree totally on Coleman and Baines. These two are very good defensively, as is Jagielka. Funes Mori is a little raw however looks a good prospect. Stones one-on-one is terrific but his concentration levels are poor.
For various parts of the season however, Coleman, Baines, Jagielka and Stones have all been injured. Throw in then Funes Mori is desperate for calm leadership to chaperone him through, and you get an inconsistent mess. This is the whole reason however it is undeniably a contributing factor. In RM's first season he had Howard, Coleman, Jagielka, Distin and Baines all playing consistently. We looked far more solid as a consequence.
Purchase an aggressive CM
McCarthy may be this man and shouldn't be discounted from the equation. He's a dynamic hassler who wins the ball back at will, when on form. The problem is that he is positionally erratic when he's off form. He chases the ball around like a nutter which, as against Utd, was all for nothing each time Utd completed a simple one-two around him.
Besic could also be this man.
For me, I doubt their abilities
at this time only because they are prone to a poor game. Look at Kante for Leicester, as an example - never has a bad game. Schneiderlin - i've seen Utd alot this season and the lad rarely has a bad game. Dier the same for spurs, seemingly never has a bad game. Last season Matic was instrumental in Chelsea's title winning side. We need someone who will consistently be 7/10 every week. They need to be able to play with and sometimes instead of our ageless Gaz Baz.
Might seem wordy and a load of tosh BUT to me the above proposed remedies are easily achieved. Whether Martinez can or will see it similarly, God knows.