Well I'm a little miffed that no one on this board was able to even make a suggestion as to what my problem was. However, since I was able to resolve it myself, I will post the problem and solution for anyone else with a similar error.
In the log I posted in my original post, these were the important messages:
rcvd [LCP ConfReq id=0x54 <mru 1500> <asyncmap 0xa0000> <auth chap MS> <magic 0x5f5a09d9> <pcomp> <accomp>]
sent [LCP ConfNak id=0x54 <auth chap MS-v2>]
The ConfNak message basically means that one of the option values I received from the destination server in the ConfReq was not what my configuration wanted. The value returned with the ConfNak message is what my configuration wants to use. In this case, the PPTP server I was trying to connect to wanted to use <auth chap MS>, but my options.pptp file was only allowing for <auth chap MS-v2> to be used. To fix the problem, all I had to do was go into my /etc/ppp/options.pptp file and comment out the following line:
After commenting this out, the auth chap MS value was accepted by my client and all was good.