How can I replace garage door opener remotes?
I fixed the exact same problem with my garage door using a general purpose relay output wireless transmitter / receiver module I purchased from eBay. The receiver module for inside the garage operates from a +12VDC power supply which I purchased for low cost from Goodwill. The normally open relay contact of the receiver is wired in across the same wire pair used by the inside door open push button. The existing push button is designed to short across the two wires that run to the garage door opener. The added relay connections need to be wired in parallel to the switch so that they short across the same wires when the remote is activated. 



The trigger buttons are small key fob type push button controls that operate from a standard type of coin battery.



Note that models on eBay change often and it is a good idea to search for a unit that comes with multiple fobs and to purchase a spare unit if you ever think you will need replacements. Some sellers will add additional fobs to your order for an additional small charge. The search to use on eBay is Wireless Remote Control.

The whole setup cost me about a third of the lower priced options that you have linked to. The unit I purchased was a two channel device with an A and B button on the fob and so one setup was deployed to run both of my garage door openers. 

These come with the remote transmit code set to some default value and it is advisable to change that code to some random code that you select. Changing the code entails some work with a small electronics soldering iron inside both the receiver and the transmitter.