After my original post, I flashed DD-WRT firmware to my DIR-825. I then enabled a PPTP VPN server on it, connected it at my main home.
The DD-WRT firmware is great. Installation was easy, just carefully and patiently follow the instructions. Router is a *little* warmer than it used to be, but working fine. Signal seems to be a little stronger, not much, not sure, but small little pockets of poor reception I used to have are less common.
To test the PPTP VPN, I used my Android cell phone (connecting on T-Mobile's data network) to connect to the VPN. I then went to a website to check the IP address of my phone, and it matched that of my home internet connection. SUCCESS! No reason a VPN client wouldn't work the same way in Mexico.
Note: There is no LT2P server included with DD-WRT. It can be used as a LT2P client, but not as a server.
Now....I also did A LOT more research on my original question. I'm still not certain of the answer, but I plan to install a *different* stock DIR-825 B1 2.07NA I have at another home nearby, and see if the stock firmware will work as a client. Because I absolutely HATE searching for questions like this, finding other people with the same question/problem, but no answer posted, I will be sure to post back here so that others can learn. I'm thinking that the stock firmware will work as a VPN client.
As for whether this will solve all my problems....not sure. The internet speed on my phone was definitely slower on the VPN than on T-Mobile's network, but I was in a poor coverage area at the time. Hard to say whether the bandwidth on the VPN (which is limited by my home network's upload speed, and Mexico's download speed) is high enough to do what I want to do, which is to stream HD quality video. I will try to drop by a public wifi connection tomorrow to do more testing.
I feel like I'm talking to myself.