There is no way of telling the UKBA that you need a few more weeks so that your fiancé can come to the UK for you to marry unfortunately. The UKBA's position on this is that you either make an application for another visa in an appropriate category or you should return home.
However, there are things that you can do to enable you to stay here and marry your fiancée.
To be absolutely certain that you would not be deported before you visa expires you would have to submit an application before your visa expires. If you did this then you would have temporary leave to remain until the application is determined.
So, even if you submitted an application which you thought would almost certainly be rejected you would be allowed to remain here until it is determined.
This would likely give you enough time for your fiancée to come to the UK so that you can marry.
There is no restriction on you marrying her. The overstay does not matter because the UKBA requirement for a certificate of approval for foreign natoinals to marry has long since been abolished:-
Once you are married to her and she is in the UK working (ie. exercising her treaty rights) then you will be able to apply for a residence card confirming your right to remain here and work as the non-EEA spouse of an EEA national exercising treaty rights in the UK. The page on this is here:-
Sometimes, people have problems convincing the UKBA that the marriage is genuine, but provided that they believe the marriage is genuine then you will not be removed from the UK and will get your residence card on the basis of the marriage even if you do not have leave to remain at the time you make your application for the residence card.
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