I'll give it a shot.
First comments I want to make are:
Equal strength forces in an urban assault is not good. The defenders have an advantage, most of the time, especially when not contained to one area of the city or one building. Although the 3:1 attack ratio is recommended, I have read of sources stating 10:1 upwards. Urban areas are extremely difficult because of their nature - 360 degrees of "anything can blow me the f- up". With such open ground anyone with an RPG can peek and shoot the Bradley within seconds. This means that infantry have to foothold before bringing in the video. Leading to my next point... This is a combined arms question. Utilizing the Bradley and Heavy Weapons Team (AT especially) is vital to success. Maneuver without their support would be fatal, none the less them taking lead is not a good tactic. There is a lot of open ground before even meeting the town. Navigating around it therefore may be dangerous, even to get a better angle of attack on it. There are also numerous road/obstacle crossings involved. I can't really tell how the terrain lies and do a good map analysis and I haven't planed CinderCity in AGES so I might be off on some points.
Let's start by splitting up the objective. Not necessarily for multiple teams but like phase lines for each initial region to hit and for communication purposes:
Red is dangerous. Especially for maneuver against the attacking element.
Orange is heavily defended residential area. Probably to put off the idea of a frontal assault. This area can be reinforced.
Yellow is the most dense urban area where the HQ and CCP are located. I suspect units there will remain in place to defend HQ.
Example 1, Western Assault (Flank):
Not a bad idea if the Bradley and Heavy Weapons Team/Anti-Tank Team are capable. This could lead to a clogged up firefight which is reinforced, none the less. These 9 buildings in orange clearing room-by-room could take a while.
Example 2, Frontal Assault:
A nightmare. No doubt would lead to the most casualties. Therefore no center-penetration is recommended.
I think another maneuver like enveloping or pincer might split the forces numbers too low if they become dispersed or too far apart. And they're already low. Concentrating them and keeping the Bradley capable and the Heavy Weapons on overwatch is a priority. There is also limited terrain to do any kind of fighting patrol structure so it comes down to ducking behind one another and avoiding bunching. Satellite patrolling or paralleling would not be advantageous.
My main points would be:
Destroying IFV and MG bunkers from afar is a good plan if capable. Countering IFV approach to outmaneuver the static bunkers and assault them is also a good plan.
Getting into short-range firefights risks not only losing a lot of men but getting clogged down where the enemy can reinforce or out-maneuver. Therefore the Bradley and HWTs should be in support of infantry, and each infantry unit in support of one another.
Infantry should use good combined arms approaches. Sending scouts forward. Checking corners and streets before moving. Covering 360 but reinforcing areas of likely approach. Infantry should also have light AT capable and towards the front of the group.
The target buildings (TBs) are big areas to clear that may also provide a greater view of the battlefield. Getting trapped/isolated or picked off in these buildings, however, is a bad idea.
The center fourway is very dangerous due to multiple IFV potential COA, infantry reinforcement and the MG nest. This place is a cluster. Destroying the IFV and potentially the MG nest will be the only way for a safe road crossing unless you find concealed angles/dead ground.
Pushing West may lead to an engagement with multiple IFV. If IFV2 has to maneuver, it is coming from an urban area which may provide cover/concealment. As opposed to IFV3 which is already in a make-do fortified area. Therefore pushing East might lead to a prolonged engagement. Infantry also has more cover from the West, both on approach and once inside where they can set up in buildings.