Re: Possibility of converting 'L' type permit to a 'B' type
First of all, be aware that you cannot apply for any permit by yourself. your employer has to do it.
regarding your situation, i very much doubt that the authorities will give you a L permit for a 6 months contract. As a NON EU, you are last in the job queue and the employer has to find that he could not find anybody in EU or Switzerland to do the job and the salary has to be high enough to justify that you really have some good skills which the employer cannot find elsewhere.
even if your employer manges to get a L, remmeber when the second employer tries to get a B permit for you, it will be assessed by the authorities as a fresh application which means the procedure is the same like a L permit. both permit cases have no gurantee of success as you are NON EU.
i think in your case it is better to wait for the employer who wants to apply for a B permit because L permit has its own problems in renting a house and getting an apartment, opening a bank account etc. search in the forum for similar threads and you will find lot of information about L permits for NON EU. there are lot of rules what you can/cannot do on a L permit, so life will be much easier if you have a B permit.