Closest in 9" would be 2.75:1 from memory.

The HK-HG 10 bolt ratios started at 3.08:1 and ended at 3.55:1, then 12 bolt from 3.73 up to 4.88. Forget trying to get any of these, will cost you way too much. You are far better off with a 9" made locally (might be time for a new tailshaft at the same time but will bolt in using your brakes or better still get made for HQ-WB drums and then upgrade your front rotors and calipers to HQ-WB). Or get a 12 bolt made by Moser in the USA with ends and axles done here, or find an old Camaro or Firebird 8.2" 10-bolt in a 2.73 ratio and get its axle tube ends changed and new axles made to suit HK-HG or HQ-WB brakes. You can buy new posi or Trutrac centres for these. You are best off with a 10-bolt in a Brougham though as it doesn't have the clearance hump in the floor and tank for a 12-bolt.

Other alternatives are shortened Borg Warner rear ends with new axles and ends or even left field stuff like Dana44 (all bits new available) or a Volvo Dana rear axle.

You could get the Chevrolet 8.2" 10-bolt in 2.56 and 2.73 in the USA but like the locally made GMH large salisbury the 2.xx ratios use a different carrier to the 3.08 and upwards examples. I'm not sure if anyone makes new gears for the 2.56 and 2.73 8.2 diffs or even carriers for them, most of the aftermarket seems to be around 3.08 and upwards.

I wouldn't bother trying to convert HQ-HJ 2.78 or HX-WB 2.60 salisbury to fit a HK, parts are hard to get for them and will cost more than doing a Commodore rear end.

The other diff that might suit is a 2.75:1 Borg Warner from a XF-XH Falcon. They are only slightly wider than a HK-HG diff so will shorten OK, get new ends and axles with the right mounts and will be more than good enough for a 307 and 'glide. I bought one out of a 1987 or so XF 5spd ute for $150, it was LSD too and in perfect order. I wouldn't use that diff behind a 350 but behind a 307 it will be better than a banjo.

I'll correct the above, I think the XF diff was a 2.92:1 but still not far from 2.78.

25 years ago the ideal solution was a shortened 2.78 sals from a HQ-HJ but given how old they are and no new bits available other than bearings it's not a great idea to invest in one.

The other nice mod to a HK Brougham is to get a Commodore or WB Statesman V8 Trimatic built and new bellhousing to suit the SBC made. Works best of your Brougham was originally console shift, if it was a column shift you could use a RH shift Triatic and use a HT-HG Trimatic column. These fit with a HK 6cyl Powerglide or all synchro 3spd crossmember and speedo cable off an all synchro 3spd. The SBC pushes the box back about 20mm relative to where it sits in a HT-HG but there should be enough movement in the slots on the crossmember. You most likely could then use a standard HT-HG V8 Trimatic or V8 3spd yellow tailshaft off a banjo car if you kept the banjo (the slightly shorter pink shaft might be better), otherwise you need a custom shaft anyway unless you use an 8.2" 10-bolt then a HK-HG SBC/AUTO/SALS tailshaft might fit of you can find one.