There should be no 'restriction' about the Historical Tester. So the converted strategy should work fine in the tester as well.
What might be the case is that there is something in the EA/strategy that is behaving differently on a demo account compared to the tester. For example, if you want to get the current time, it is always 'in the past' on a demo account. Whenever you call the function to get the time, the returned value will be a couple of milliseconds behind.
If you execute the same code in the tester, and suppose you test between 2012-01-01 and 2013-01-01, the current time (2015-01-19) will be a date in the future (compared to 2012 and 2013).
If there is anything on the code that uses such thing (makes decision on date/time), there is a chance that it is going wrong in the tester.
And this is not only involving the current time, but for example the date+time of the last bar/tick for an instrument.
I haven't looked on the code, so I cannot say that this is the problem. This is just a possibility.
I suggest further on to create a topic in
here, so Support is aware of your issues. And they can probably help to get you further.