Wa aleykum salam
May Allah bless you.
Sheikh Yusuf Qardhawi and the European Council for Fatwa and Research issued a fatwa (with conditions) allowing the use of a conventional mortgage.
Some people use the fatwa issued without considering the conditions laid down in the fatwa itself. This is clearly a misuse and in some instance a manipulation of the fatwa to seek personal gain.
In your case, if you believe that you fulfilled all the conditions of the fatwa before taking the mortgage then there is no issue with it.
As far as the remortgaging is concern, if you have the possibility to switch to an Islamic mortgage, then by all the mean this would be the best thing to do.
When would be the best time to do it? If your financial situation allows it, then you should do it as soon as possible.
If on the other hand, you were unable to remortgage with an Islamic bank lender, then you should just carry on paying your conventional mortgage as you would normally do.
And Allah knows best!