Your adjuster is handling this claim properly.
First of all the plaintiff attorney must convey the adjuster's offer to his client. If he hasn't, he his in violation of attorney ethics, and he's afraid his client will accept it.
The plaintiff attorney wants a prolonged extension because he knows he has a lousy case and if he has to actually proceed with the litigation it will cost him money.
He is going to get a percentage of any settlement he can effect. Usually about 33.3% The less time and resources he devotes to this matter, the more he collects.
Some of these scumbags actually try and charge their clients for "administrative costs" and so they get to keep even more of their share.
The only reason a plaintiff attorney wants an extension is because he realizes he has a loser and doesn't want to invest any money in the case.
I understand why you are concerned, but this case will never go to a jury. Never.
It will be settled and it will be settled within your policy limit.
Just in case, tell me the following:
What are your policy limits?
How much has the plaintiff attorney demanded for a settlement?
You can get obtain the answer to the first question by looking at your policy or asking the adjuster
You can obtain the answer to the second question by asking your adjuster. He must give you an answer.
Get me the answers to these two questions and I can advise you further.
Obviously anything can happen, but I feel very confident that you have nothing to worry about.