Heat is going to be your enemy here. You should get a tight handle on the current draw of the motor.
The L293 won't deliver the current you need. the L298 will do it though the limit appears to be 3A - right at your limit. that's a little troublesome. neither package (multiwatt or powerso) are super easy to prototype with. with 3A of current, the L298 will dissipate a very large amount of heat Vsat at 2A is 4.9V - that's 9.8W. Take it up to 3A and it's going to around 15W. I suspect you can get by with passive cooling (heatsink) for 1A draw but 2 or 3A draw will probably need forced air.
alternatively, you could build an h-bridge with mosfets. Mosfets with a reasonably low Rds will give you significantly lower heat dissipation. For example, mosfets with an Rds of .1 ohms will dissipate about a watt each at 3A. It would probably get by with a smallish heatsink. Plenty of plans on the web.
Phil