bulk tf up
(up your melee stats, have a good shooter with an automatic weapon and lots of bullets in case of emergency, and hope you roll some rare locations, i.e. Haunted Mansion with OP weapons)

You should also go for rescue missions, usually you'll get some skill training or goodies after!

as said, BULK TF UP. choosing which stats to buff is super important. here's my own personal strategy i like to use when deciding which stats go to who:
start with a support character you'll take control of for the whole run and keep the rest of the party combat-focused. focus on upping fitness and strength for the fighters while the support focuses on medical, mechanical, and shooting. the support is to act as a catch-all for getting through all text events, and with their high shooting, act as a last resort for sieges.
all the fighters will need to do is have high enough stats and good enough weapons that they can get the job done. in my own personal experience, even just one 3-6 stat fighter with a good weapon and two 0-3 stat ones with whatever non-breakable weapons you find on the ground will do the trick; stats are very important, but the whole reason i employ this strategy is because 3 fighters working together is incredibly effective, no matter who's involved or what their stats are.
when your fighters have officially reached the status of being able to get the job done, you can set their command to FIGHTIN' and will have basically no need to change it for the rest of the run. either zombos will be sparse enough that your party running after them isn't a big deal, or plentiful enough that taking them out is a high priority. and once you've reached the status of able to get the job done, that's really all you need to get to canada!

apologies for the essay. i really like this game. LOL

For extreme modes, I prefer using one thick, tough, bulked melee character coupled with a skilled character

like T*S*T*C* with either 'sound sleeper' or something that adds more strength, then another character like surgeon with something else like explorer so they can shoot and provide use in RPing events

RPing events are also nastier and more brutal and deadly.

For that, Paranoid characters make *great* teammates

I think I beat the extreme modes w a T*S*T*C* + SoundSleeper, that way I can 'Chop wood' and do other things that leave the team exhausted, but now that they have "sound sleeper" they can perform the following day. Putting Sound Sleeper on the melee character is the best, there's always a time where you don't get sleep or need to stay up at night.

But as for sieges:
with a T*S*T*C* character, I can often rip out a sink or toilet and fling that in addition to tossing all furniture. Usually, if you just keeping dying and restarting, you'll get a good starting run where you get lucky and can get a few extra points in Strength. TSTC characters can get strength so high they can toss fridges and other big heavy things that dont bust in one go. Once the TSTC character is strong enough to toss objects like that, they merely smash the room once or twice w big thing while teammates sweep up.

Don't be afraid to risk *everything* to win big, that's how I beat those modes, risking a big one and getting 148 food + 340 gas in one trip, there are locations and events that turn wildly lucrative in extreme modes,
so why not start with a character that has a wildly high strength score
T*S*T*C*