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I do have an RCA portable tube radio which has space for two 1.5 volt cells in parallel (those old kind of 1.5 volt cells which are about the diameter of a "D" cell but about 1 1/2 times as long) but I've read that parallelling cells like that can cause problems where a stronger cell can end up discharging through a weaker one...not sure if that is really true or not. Using a diode to isolate the cells wouldn't work I wouldn't think because the voltage drop of the diode would eat up most of the 1.5 volts.
I read that a "D" cell has 12,000 milliamp/hours and I figured the total filament draw of the radio is 400 ma so the cell should last about 30 hours, or what some people have said the 9-volt batteries would last in this service.
What would be great is if you could get the really big 1.5 volt cells with the screw terminals...if they still make them I'm sure they're really expensive now.
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