As it stands, the SL system is woefully inadequate in punishing 'bad' behavior, especially as it doesn't discriminate between who doing what to whom and only affects the Copbot system. Faction sympathies have little or no impact on runner lives other than with your own faction.

Before I make any suggestions however, we should be aware that much of this is probably futile for the simple reason that alts are available. People can easily have 'good' backup chars to hunt, tradeskill, poke, buy, etc. and thus any consequences imposed on their 'main' chars are somewhat meaningless. I would prefer a single slot server, but that probably won't happen for a long time.

Firstly, Soul Light.
I say get rid of it. It's indiscriminate and unrepresentative much of the time.
The question of what Copbots respond to is somewhat linked to arguments about anti-CA runners being allowed inside the city (why wouldn't a Copbot open fire on a TG runner operating inside the city limits?), safezones and similar. Unless a time comes where anti-CA factions are not welcome in the inner city (I won't say which I am in favour of), I'd say set Copbots to fire when a runner reaches either -16 average in all symps or -32 average in CA-allied factions.
Reprogrammed Copbots would follow something similar based on the factions where they located.

The main part is Faction Sympathy, which as I see it needs to affect far more aspects than it currently does. Including but not limited to:

GR costs/access:

Dependent on both the symp of the owning GRs going from and two.
Going from a CA GR to a TT GR with low symp in both would cost you a lot more than normal.
GR costs on death would purely depend on the location selected.

At -32 (maybe lower?) in the faction of the destination GR, travel would be refused.

P1: CA
P2: PP?
P3: DRE
P4: NExT
VR1: BT
VR2: TT
VR3: CA
PP1: TSU
PP2: BD
PP3: CS
OZ: None?
DRT: NExT?
BD: CM?
Crest: Trader Union?
MB/TH/Canyon as you would expect.

As this can't be circumvented by alt use, this is probably the main way symp would affect people's lives.
This would encourage people to keep tabs on and try to increase faction symps, though it would have to be balanced to assume a certain symp level.
Symp gain in one faction should also cause a loss in one or more other factions to help prevent people 'abusing' the system with 100 symp in all factions (though perhaps this could be possible but extremely difficult to attain). Remove the auto-symp gain while idle. Of course, you could make it so that extra positive symp (50+?) has little or no effect on prices.

Vendor prices:

As with GRs, each vendor has an assigned faction. Symp with that faction acts in a similar manner as Barter.
Most of the shops are fronts for the main factions anyway. Faction HQ vendors would need 90 symp like FSMs.
Refuse trade at a given level?

Crytons (Tools): CA?
Crytons (Imps): BT?
A&W: TT
HEW: TT?
Medicare: PP
Brothers in Arms: CS
Boobs and Guns: TSU?
Fist Weaponry: TG? Depends on if they (Fist) remain in the city.
Techangels: FA? Same as with Fist.
Drug/Medical vendors in PP/OZ/Canyon: BD
Furniture/Real Estate: DRE/BD depending on location.
TH Traders: FA
ASG: NExT
MB: Combination of the above and CM or just CM?
Canyon: As MB but TG.
Yos: Trader Union? Dependent on shop location?
OP Vendors: Trader Union and/or owning faction?

Guard reaction:

Low symp in allied/neutral factions to cause their guards to attack as if hostile (-32?).

One thing that could be asked about all this is wouldn't it be unfair to runners in a given faction or another faction has an advantage in a certain area?
Well yes, but then we have to look at faction distinction (which is a matter for a whole raft of threads). There's almost no difference between the factions in terms of the way their advantages, disadvantages, style and themes affect game play.
TT are a weapons manufacturer, yet this doesn't give their members better access to weapons.