From your list as posted, I'm thinking that you set up the platoon in the back and camp something while the vets go barrelling into the center of your enemy's formation with the Demolisher as cover. The Tau player asplodes the Chimera and then vaporizes the guys inside with Fire Warriors. He also prioritizes the Demolisher. Suddenly you're in a long-ranged shooting war with the Tau and that's not a fun place to be.
Start by looking at each section of your force and ask this question: "Why is this here?"
General things:
Take Camo netting on every tank you can, except maybe things that you know you can keep out of LOS. Totally worth it. Yes, a buffmander leading Broadsides is going to make that not matter, but Buffmander is synergistic hax anyway (and should be your first kill target). Take Heavy Flamers on Chimeras as the hull mount. Generally worth it. On a transport, you'll usually get more mileage out of the flamer than the bolter.
Specifics:
HQ
Why Yarrick? What is he doing for you that a bog-standard LC won't? Or a Company Command Squad? Or a Tank Commander? Taking a CCS lets you take an Astropath, which gets you access to a roll on Telepathy (which has one of the most broken powers in it, Invisibility). The Primaris power of Telepathy isn't bad either if you can get into range with it (witchfire fear cannon that can erase Broadsides). If your answer is "because Yarrick is cool", I understand... but know he's soaking a lot of points and is probably not actually pulling his own weight. Special characters are a strong spice: you need to build the list around them to get good things out of them. Also, use sparingly for narrative games, not as a crutch. A CCS can hang back with your Infantry squads as well, giving "bring it down" orders to boost the effectiveness of autocannon fire, and you can slap another heavy weapon into the CCS if you want to go that way (at a better BS, too).
What's the Enginseer doing with his life? Sitting in the back with the LRBTs and playing mechanic? Are you planning on using him for PotMS (there's nothing here that would benefit from it).
Can't argue with the Primaris Psykers. Good support models. However, if you have to skim points from somewhere, I'd drop one of the two (or reduce a Mastery Level) or your Enginseer and/or his Servitors.
Troops:
I'd recommend swapping a meltagun for a heavy flamer in the vet squad. You can't fire more than 2 out of the hatch anyway, and the flamer is a good clutch defense. Also, if you do manage to get close to Fire Warriors, they burn very nicely. Also consider shotguns and carapace armor on the Veterans. If you're in the Chimera, you can use the lasgun arrays anyway, and being able to fire everything and charge is useful. Give that sgt a bolt pistol (or plasma if you like living dangerously) if you give the squad shotguns, a boltgun otherwise. Boltguns can be harvested from Scout Marine boxes, combine them with a cadian lasgun arm set (or possibly catachan, but might look weird). You can get boltguns for real cheap everywhere (or trade for them, most people with Scout marines take shotguns on them and the two kits share an arm, making the boltgun arm nearly useless).
Also, take Krak grenades on everything, just in case you need to charge an opponent's tanks and deal with them that way.
Are you taking Flakk missiles on the MLs in the infantry squads? Going all the way to Flakk is one of the only reasons I generally consider MLs in line squads anymore. Better to give them an autocannon (more shots for the crap BS) or a heavy bolter (even more shots) or eschew the heavy weapon and pick up the plasma (and be able to move). You could also consider a HWS, but I generally only take those as Mortars and place them completely out of LOS.
You might want to consider swapping the entire platoon out for two Veteran Squads with heavy weapons. Better BS, and you can give them either camo cloaks or carapace (or both) to boost their survivability. You're not actually doing anything with the platoon as it stands that couldn't be done with Veterans. If you can free up some points, you can make them better at not dying to enemy fire, too.
Elites:
Consider Ratlings if you find yourself with some points. Decent models that infiltrate and sniper weapons are useful against Riptides and all manner of things.
Fast Attack:
Not crazy about the MLs on the Sentinels, maybe autocannons or plasma? It's just that the BS is not great enough to make single-shot weapons that aren't blast reliable (and frag missiles are not what you bring the ML for). A Hellhound is also nice, but is a fire magnet (and rightly so) for Broadsides and other antitank weaponry. You can pack a Multimelta on them (and/or take the devil dog) and get a very speedy melta death machine.
Heavy Support:
You have a LR Demolisher with with guns other than what it comes with. Why? The multimeltas aren't going to hit nearly often enough on SS when you fire the big gun, and you won't hit nearly enough on normal BS for it to be worth not firing the big gun. Lascannon, I'm 50/50 on. It's got range on the demolisher cannon which you can use while getting into range. The standard Russes are good infantry-clearers but can't kill tanks efficiently. Also, take the Lascannons off of the standard Russes. You've already got a big gun on the thing and 95% of the time you want to shoot the battle cannon anyway.
Either drop the Demolisher and replace it with a Vanquisher with the same secondary weapons (dedicated tank hunter), move it and the LRBTs into the HQ slot and make the Vanquisher a tank commander (Pask if you have just got to have a special character in the list). You probably want to lose the mulitmeltas if you're keeping it with the Russes and planning to keep range. You still get to split-fire (most of the time) the Vanquisher, but you can keep the standard russes in front to absorb fire. Or you can flat-out (if you need to) or pop smoke and get your guns off. All of which are good things. Or take the Demolisher, give it a punisher cohort (you will need to drop Yarrick to make this work), give the punisher the multimelta sponsons and make them a Tank Commander squad (give the Tank Commander the Punisher, if you bring Pask it's evil). Also drop the lascannon from the Demolisher in that case, you can use Tank Orders to flat out and get into the fight more quickly.
I'm not crazy about the Manticore myself, but it does have a use in clearing medium infantry from the field. A trio of Wyverns, I think, is even better at this job though and will get more hits on single targets. With three Wyverns, it's *very* likely he won't have any infantry left after a couple rounds of shooting. They're that vicious.