At that point you might as well go to a lead acid (or gel) cell, or even lantern batteries in weight and size
You run into a cost vs size issue, Lipo packs are small for the juice they push out and they are designed for high drain, but they are also initially more costly... But then again they are rechargeable while most people won't bother recharging D cells so over the run the Lipo pays for itself pretty quickly over name brand D cell purchases...
You can get 5000-6000mAh lipo packs for about $30 a piece, get two so you can charge one while using the other... As KJ6EAD the run time of D cells is about one hour at that drain, the Lipo at 5000mAh (even though less rated capacity) should perform as well at that drain rate due to design... A 5000mAh pack drained at 3000mA is only 0.6C for that pack, most lithium packs are rated for 1C or more many reliable up to 3C... Of course that isn't solid data, run time will depend on several factors, and battery companies love to overestimated capacity... But, regardless lipo packs perform better in high drain situations...
When you factor in that 5 'name brand' alkaline D cells is going to cost you $2-3 each cell or about $10 - $15 a load up, it won't take time to recoup the $30 on the Lipo investment, heck it won't take long to recoup a $100 lipo investment...