Let's look at this differently. You have a empty engine bay , you wanna keep the price at 3k. Mpg take priority over performance. What engine?
Starting from scratch? A 6.2 will fit that application. Starting with a 3000RPM cruising speed? That's a definite 'no.' Keep the 6.2 below 1800RPM at cruise if you're looking for mileage.
A 6.2 can be a very cheap and easy engine swap, especially if you find a $500 donor rig. But $500 5.3 rigs are out there, and you might find one of them is just as good a platform for your intended purpose. That engine would be much happier with your gearing.
But, most importantly, look into overdrive and/or axle gearing. None of the engines you mention will cruise efficiently at 3000RPM.
