Yah that panels is done, Id suspect those two breakers you are looking at too. The heat did not just stay there it will have travelled down the bus a bit too. TBH depending on the age just get an entire new panel AND new breakers, They are only like 15 bucks each and it's not worth the hassle if they don't fit the new panel just right etc etc. Your main cable coming in from the weatherhead, How is that? did you crispy that. Do NOT let them convince you that they can 'resleeve' that little bit of insulation there if it did burn back, that is BS, if it got that hot to burn the insulation you crystalized the copper / cook the aluminum too and it needs to be replaced. Whether they have slack in the bend and a bit of 'pull' or run that termination from meter to box they'll have to see.
This is entirely up to you but if it were MY house, at that point, THAT is an insurance claim and they are replacing it ALL, NOT ^%ing around. Now a disclaimer, I worked as an 'electrician' to give you the easy title to understand, in the Navy for 21 years, and also worked as an Instrumentation and Controls / Operator / Maintainer in a power plant for another 18 years, so I may be a bit 'sensitive' to electrical damage as I have seen many things get BTFU, often times from 'Quick Fixes' so may be a bit hyper sensitive to electrical damage
1500 dollars is actually pretty cheap TBH. They have to pull all those wires out, pull the old panel out, and shove them all back in and land them in the new panel. That is also something that they are probably going to have to pull a permit on too. Also depending on how your house is set up, they MIGHT also have to pull your meter can from the power company. This will involve letting them KNOW that happened. SAVE your receipt and call them once it is done with so they can come and inspect (basically just a formality) but more importantly, put THEIR seal back on your meter box. If they see a strange seal on it, that is tampering, and can cause you many nasty issues.
Also YES I KNOW you want your juice back on, but unless you KNOW this electrician and KNOW he's good and honest, don't be afraid to shop around.
Since it's heat damage and insulation compromised on the main bus, Id have to advise AGAINST backfeeding thru a dryer / water heater outlet for 'temporary power'
Sorry to get long winded, but with stuff like this, since you are AT this point, it's just best to do it right and get it ALL done at once up front.
Aaron