I know this will likely go over a lot of people's heads, but I've got an interesting thing happening, and I'm at a total loss to explain it.
To start, I'll point out that my server configuration is a little different than the average person's, for I have the following setup:

First off, I'm running Ubuntu 16.04.1 x64. The server currently has three network cards. Their configuration is as follows:
eth0 - 1000mbit to a 5-port switch - Modem #1 & main WiFi WAN connect at 100mbit each
eth1 - 100mbit directly to Modem #2
eth2 - 1000mbit to an 8-port switch - Modem #3 connects to the switch at 100mbit, and the trailer's WAN connects to the switch at 1000mbit
eth3 - 100mbit direct to Modem #4 (Coming Soon)
Lines 1, 2, & 3 are currently serviced with a pre-Y2K non-FTTN legacy DSL service, running on a 4032/800 fastpath profile (although they're getting upped on Tuesday to 5056/800 interleave). When joined together, I'm getting just over 10mbit down, about 1.85mbit up. Modem 1, 2, & 3 in the equation (which are the only ones with service currently) are identical TP-Link TD-8816 modems, and the 4th modem that will soon be added into the mix is a Thompson SpeedTouch 516.
Now here's where things get interesting… The server bridges all 3 modems together, and when connected through all 3 modems, I can use Traceroute directly from the server with no issue. I get the following:
noel@mail:~$ traceroute teksavvy.com
traceroute to teksavvy.com (173.246.155.216), 30 hops max, 60 byte packets
1 206.248.154.121 (206.248.154.121) 22.423 ms 22.383 ms 22.612 ms
2 ae0-2150-bdr01-tor.teksavvy.com (69.196.136.172) 22.597 ms 22.833 ms 22.819 ms
3 ae8-0-bdr01-tor2.teksavvy.com (206.248.155.9) 22.805 ms ae1-0-agg01-tor2.teksavvy.com (206.248.155.14) 23.038 ms 23.023 ms
4 ae0-2170-agg01-tor2.teksavvy.com (192.171.59.98) 23.510 ms cdn.teksavvy.com (173.246.155.216) 23.485 ms ae0-2170-agg01-tor2.teksavvy.com (192.171.59.98) 23.723 ms
noel@mail:~$
As well, in ICMP mode, I get the following
noel@mail:~$ traceroute -I teksavvy.com
traceroute to teksavvy.com (173.246.155.216), 30 hops max, 60 byte packets
1 206.248.154.121 (206.248.154.121) 9.762 ms 10.225 ms 11.364 ms
2 ae0-2150-bdr01-tor.teksavvy.com (69.196.136.172) 13.096 ms 13.911 ms 15.086 ms
3 ae1-0-agg01-tor2.teksavvy.com (206.248.155.14) 16.359 ms 17.200 ms 20.284 ms
4 cdn.teksavvy.com (173.246.155.216) 19.434 ms 20.696 ms 21.418 ms
noel@mail:~$
Now here's where things get a little interesting. When I am on say my laptop connecting through the network then out to the same DSL lines through the server, I get these same results (with a couple of extra hops). As soon as the server has established a PPPoE link through modem 2 and/or modem 3 however, things get a little strange (as in this example):
noel@New-Laptop:~$ traceroute teksavvy.com
traceroute to teksavvy.com (173.246.155.216), 64 hops max
1 192.168.100.1 (router.trailer.ohsweken) 0.365ms 0.608ms 0.469ms
2 192.168.0.1 (server.ohsweken) 0.656ms 0.565ms 0.482ms
3 * * *
4 * * *
5 * * *
^C
noel@New-Laptop:~$
What gets more interesting, is that when I add ICMP mode to the mix, it works just fine, as in this example:
noel@New-Laptop:~$ traceroute -I teksavvy.com
traceroute to teksavvy.com (173.246.155.216), 64 hops max
1 192.168.100.1 (router.trailer.ohsweken) 4.529ms 0.391ms 0.316ms
2 192.168.0.1 (server.ohsweken) 0.633ms 0.635ms 0.620ms
3 206.248.154.121 (206.248.154.121) 11.241ms 10.595ms 9.976ms
4 69.196.136.172 (ae0-2150-bdr01-tor.teksavvy.com) 10.934ms 9.878ms 10.258ms
5 206.248.155.14 (ae1-0-agg01-tor2.teksavvy.com) 16.042ms 11.698ms 9.858ms
6 173.246.155.216 (cdn.teksavvy.com) 10.114ms 11.691ms 10.520ms
noel@New-Laptop:~$
Does anyone have a best guess (or even better, actually know) as to why this might be? I'm very confused and it's driving me absolutely bat shit crazy!
Please help… If you can.