Making a program to create the special packets is actually pretty simple, and you don't need to use PCAP or other magic to set the TTL. For example here is a quick hack in C that does the trick pretty simply. It'll run in Linux, someone could probably make a Windows version, or build it with Cygwin/...

I'm a Cisco-certified network engineer and software developer. Feel free to PM me for further questions. You may want to read that RFC again. It's talking about a checksum of the header, the one in the IP header. The UDP checksum includes the data (this is another checksum) ... so it definitely can...