Is tire slime/goop a viable long-term way to deal with it? (I'm not thrilled with squirting that stuff in there, but if it would mean being able to put off buying a new tire, I'd try it...)
Or should I just chuck it and buy a new rear tire?
The world is full of warnings... like stick to 4 wheels because two wheels will kill you...
1 Submerse the tire in water to pin point your leak...
2 If you use slime... you'll regret the mess come tire change...
3 I recommend rope type plugs as opposes to the inside mushroom type plug...
Here's all the poop on wether to plug or not...
Minor tire repair is limited to an area of three quarters of the
normal section width. The maximum diameter of penetration damage
and/or cracking at the base of the injury should be no greater than
3mm. The repair patches must not overlap. If a tire is deemed suitable for
repair (by a professional) then follow the instructions provided by the
manufacturer of the repair material.
For permanent repair,it is only recommended that small punctures
restricted to the tread area be repaired, using a rope type plug. The
current condition of a tire is important in determining whether a tire
is suitable for repair. Some damage limits include: if the tire has
reached its minimum tread depth as indicated by the TWI (tire wear
indicator); ply separation, separation of inner liner and or cutting
of ply cords by penetrating object; brittle or cracked rubber caused
by exhaust heat; broken or bent bead wire, damaged bead zone; damage
caused by under-inflation; softening or swelling of rubber due to oil
or chemical attack; punctures too close together; damage or previous
repair of a puncture outside of area specified for suitable repair.

My screwed Rennsport... boo hoo

My plugged Rennsport that covered 2K miles and not in moderation either...
keep it a secret but it's seen over a buck 40 more than once...

Inside the Rennsport for proof that the rope type plugs stay intact whereas
my mushroom tyre plug started to come unstuck

I'm using the BMW tire repair kit with the rope type plugs

Nylon Rope type plugs found at any auto parts store...

I don't recommend the mushroom type plugs...

What the Manufactures say about tire repairs:
Metzeler quote: "According to the specific regulations of different
country governments, a general recommendation regarding tyre repair
cannot be given. For your country, please refer to your distributor.
In case a repair is permitted, METZELER is only recommending the
repair of small punctures restricted to the tread area using a
mushroom head type plug. The repair of a punctured tubeless tyre by
means of fitting a tube is not permitted" .
Dunlop quote: "Any puncture or injury to a tire's tread area obviously
affects performance and safety. Proper repair is critical. The
puncture must be repaired on both the inside and the outside of the
tire. Because all parts of a tire are engineered to function as a
single unit, any repair must take that into consideration. Only
small, straight-through 3/16" diameter or less punctures in the tread
area may be repairable, if no secondary damage has occurred."
NOTE: A tire repair can be properly made only if the tire is removed
from the rim; a thorough internal inspection is carried out; and the
repair is made from the inside out. A repair must fill and seal the
injury, i.e. vulcanized plug and patch. Only specially trained
Technicians are qualified to repair a tire. Do not attempt to repair
it yourself.
Dunlop Safety Advisory, Speed Rated Tires: Repaired tires must not be
used in excess of posted speed limits, in race or other competition.
Speed ratings are not valid for repaired, re-treaded, under-inflated
or overloaded, excessively worn, damaged or altered tires. "
Bridgestone quote: Riding on an improperly repaired tire is dangerous.
An improper repair can cause further damage to the tire. It may
suddenly fail, causing serious personal injury or death. To be safe,
go to your local dealer for proper tire repairs.
Before having a tire repaired, tell your local dealer if you have used
an aerosol fixer to inflate/ seal the tire. Aerosol fixers could
contain a highly volatile gas. Always remove the valve core outdoors,
away from sources of excessive heat, flame, or sparks and completely
deflate the tire before removing it from the rim for repair.
* Never repair a tire with less than 1/32nd inch (0.8 millimeters)
tread remaining. At this tread depth, the tire is worn out and must be
replaced. * Never repair a tire with a puncture larger than 1/4 inch
(6.4 millimeters) in diameter. Such tires cannot be properly repaired
and must be replaced. * Repairs of all tires (radial and non-radial)
must be of the plug and inside patch type. Using plugs alone on any
type of tire is not a safe repair. * Never repair a tire with a
puncture or other damage outside the tread area. Such tires cannot be
properly repaired and must be replaced. * Any tire repair done without
removing the tire from the rim is improper. * Tubes, like tires,
should be repaired only by a qualified tire service person. * Never
use a tube as a substitute for a proper repair.
A tire's speed rating is void if the tire is repaired, retreaded,
damaged or abused, or otherwise altered from its original condition.
Thereafter, it should be treated as a non-speed-rated tire.
Michelin quote: In case of a flat, take the tire to your Michelin®
motorcycle tire dealer. Only a professional tire technician has the
expertise to properly inspect a tire for damage and determine its
repairability.