Back testing with different spreads for Entry/Exit?

Of course. It is just logic & conditions.

Even with back testing? Could you please explain how one would go about coding the EA to use a different entry/exit spread rather than the spread set in the strategy tester?

Do you know how to get spread? If you know, just put some condition to fulfill.

Spread is fixed with the Strategy Tester.

It's possible if you manage the spread, bid and ask price inside your EA. You have to monitor your trades and close it yourself, not by sl/tp.

MT5 have varying spread as it's saved in history data (1 value by minutes data).

Tickstory allows you to import tick data into MT4 for use with the strategy tester.

You can specify the spread you want to be applied to that tick data, but it will be constant throughout that tick data.

For example, while strategy tester may want to apply the last known spread of 30 points, you can download tick data with a spread of 20 points and run your backtests on that.