If it worked properly until recently, then I would suspect you have a problem with a pinched wire or two....or maybe someplace the turn signals and brake light have a common ground that has come loose.

I'd have to look closer at the schematic, but although I will certainly bow to those who have a greater knowledge of this specific bike...seem a bit weird to me that a loose ground would cause that.

In a series circuit, all of the bulbs would be in series, connected to the same hot. I would THINK that each of our bulbs gets it's hot from a specific place, i.e., the turn signal switch, the brake switch, etc. If all the lights are coming on when you use the turn signal, it would seem more likely that when you wired them up you used the same hot for all of the bulbs.

I did notice that he said he swapped all of his switches out with aftermarket parts.

Ours is a pretty simple circuit, but if you dont know electricity or wiring then it's never a good idea to swap out all of your parts at one time, then close it all back and see if it works.

When you turn on the left turn signal (on a stock Savage), ONLY the left front and rear turn signal "hot" wire should get voltage from the blinker relay. They each have a specific hot lead.
If say, you tapped into that wire to use for a hot for all of your lighting, then yes..the blinker relay would be more than happy to flash every light on the bike.

Personally, I think you have a "hot" problem, not a ground problem.  You are sending power (through the new aftermarket switch) to all of the lights on your bike (except maybe the license plate bulb...as I believe that is a different circuit entirely) at the same time, causing them all to blink.

Do they blink at the normal speed? (I would think they blink slower ).

If you take all of the lens covers off and remove one bulb at a time starting with the front left turn signal bulb(they get hot, turn off the bike between bulb swaps) then try the turn signals, left...then right.
If removal of any one of the bulbs causes you to lose ALL of your lighting, then you grabbed the wrong wire to use for voltage to your new switch setup.