Who makes budget speaker cables which are truly “good” or “exceptional” in quality?

Blue Jeans Cables Belden 5T00UP 10 AWG (white or gray jacket) with their Locking Banana plugs that are Ultrasonic welded which allows it to literally fuse the copper wire to the brass banana plug body without using the heat of conventional gas or arc welding, for a tremendously strong physical connection, low contact resistance, and low susceptibility to corrosion.  Custom made to your length requirements its the best value in cables out there.

For years I was quite happy with Auvio 12 AWG premuim speaker wire ($0.48/ft; but, alas, no longer widely available). My weakness is that I spend too much time on these forums and eventually give in and buy something of questionable value.
Recently I bid $80 on a $1,200 pair of Zu Lubtec cables. I think the improvement is worth $80. I'm glad I didn't spend $1,200!

Take a peek online at Cabledyne. Excellent 
cables and excellent value.

Beside the excellent low-cost heavy 10-12awg proposed by Van Damme, Belden, Monoprice, Douglas,etc... I would say Canare 4s8 is a best buy.  It is 13awg, so a little more resistive, but it seems, it feels like it makes my LS50s sound a bit smoother, for the better.
Impeccable quality of construction, PE insulation, starquad, flexible, made in Japan.

Who makes budget speaker cables which are truly “good” or “exceptional” in quality?

You do!!

@unreceivedogma is right. With two caveats:
1. Unless you are running long cables, in which case you want to minimize inductance, by having the two conductors as close as possible.
2. Terminating connectors are a tradeoff. While they ensure a good connection to the speaker and to the cable, which is good, they introduce an extra pair of junctions, which is not good. But spades or bananas are convenient ... If you decide to go without, which is a good idea, just make sure that the copper at the connection points is clean and stays that way - Vaseline helps there. After a while, trim off the ends and repeat.

IMO. YMMV.