Regarding the first motor, unless you can find out it's k/V (rpm/volt) or it's rated RPM at it's rated voltage, there's no way to know for sure what speed it is going to run at, and thus to know if it's suitable for your project (or what to calculate the gearing to be).
Regarding the second motor, it would probably do pretty much anything you want. But it will also be pretty heavy, and will require a brushless controller to run it--preferably a hefty one, which will not be all that cheap (Lyen sells some that will probably let you run it very hard; ask Evoforce about the big one he's got on his bike with an X5303 (I think it is).
You'd need to figure out the gearing ratio for it though, just like with any other motor you want to use on there. I'm not always great with math, so I may make serious mistakes in calculations (or even the formulas needed to do them with!), so someone else is gonna need to check my conclusions. I recommend you check them yourself, too, before you actually change anything or buy parts.
We've gone thru ratios you might use on there before:
http://www.endless-sphere.com/forums/viewtopic.php?p=399775#p399775
dealt with the ratios on your original motor, but later on
http://www.endless-sphere.com/forums/viewtopic.php?p=438122#p438122
you ended up going back to that same ratio and it didn't help, which confuses me.
Gtadmin did some calculations:
http://www.endless-sphere.com/forums/viewtopic.php?p=438435#p438435
and then some subsequent discussion leads up to a possible conclusion that you'd have to gear it way down to keep from melting it, and just accept a lower speed out of it.
No gearing/calculation has been discussed in any detail on your newer motor (which also smoked).
One thing I may have missed but didn't see, is what kind of terrain you're riding on. If it is hilly, and not flat, then it's going to take significantly more power to go up the hills than to run on the flats or go down the hills.
Plus, the faster you go the more air resistance, especially once you get up past 15-20MPH; it starts making definite increases in the amount of power you use to get to and stay at a speed, even on the flats in no wind, and motors get hotter.
What I would do is use the previous calculations to determine your gear ratio, if you know the rated loaded RPM of your motor at the voltage you'll be running it at. If you're not sure how to do that calculation, someone cna help with that, but we do need to know the motor's specs to figure out what it should be driven at to get you the speed you want without cooking it. There's no detail on the ebay auction, so no help there.
I thought I saw a reference to a wattmeter in one of your battery posts. If you can use the wattmeter to determine your power usage with the mtoor itself, whiel riding, it would help tremendously in figuring out what setup you actually need.
I think the Mars motor is way overkill, though it would almost certainly do what you want with room for more.
If you're willing to do some DIY, you can get a powerchair brushed or brushless motor that will do quite a lot of work, for probably very little or even nothing, if you can make friends with your local powerchair repair places, and show them your project you want to use it on. I'd bet that at least one person there would love to see some of the motors they just throw away turned into something useful.
(you can look thru my CrazyBike2 early build thread and http://electricle.blogspot.com blog for some of what I've already done with such motors, and then at my Powerchair Motor thread for info on the latest stuff I'm working out with a brushless one).
You could even use a hubmotor as a middrive; several people on ES have made them that go thru the gears of the bike or just a single-ratio leftside drive like you've been doing, and they've worked out fine, even on hills.