The Federation Council initially authorized NCC-1743 for U.S.S. Xanthii as part of the large Achernar class appropriation on stardate 5930. As with many ships in this class, as more and more hulls were cancelled she underwent several name changes - first to U.S.S. Panjsher and finally to U.S.S. Franklin. Frankling commissioned in 2266 in the standard Achernar configuration before refitting several years before 2279 to the Constitution (II) specifications. Some time after 2280, she refitted again, this time to the CB heavy command cruiser configuration. There's no indication of whether or not she had the command cruiser package prior to this and she was probably a standard CA in terms of Star Fleet Battles statistics (then a CA+ after her refit). 

In 2295 (+/- 5 years) she was refitted again, this time to the Enteprise II (CX / Enterprise mk IV) configuration. She continued to serve in this configuration until 2318 (+/- 5 years), when she was decommissioned and scrapped. Unfortunately, beyond her maintenance history we don't have any records about Franklin so we can't really delve into her adventures.

Now, if you recall the discussion of 1742 and know the source material, you might be wondering why I went with the FASA name here and the SFB name for 1742. Honestly, any of the three apocryphal names for either ship could be the real one. However, we have accounts of many ships named U.S.S. Franklin, including one ship that appeared on screen in Star Trek Beyond. This struck me as an indicator that of the three potential names, Franklin was most likely to win out in the political and procurement arena. 

U.S.S. Helin is a bit of an anomaly. The only reference to NCC-1692 in the usual expanded universe sources is to U.S.S. James Edgar Johnson, an NCV type shuttle carrier that would have been a sister ship to U.S.S. Richard Bong. Unlike Bong, the limited information we have at our disposal indicates that she was new construction rather than a refit. However, we have a canonical name for 1692: U.S.S. Helin. It appears on props for Star Trek 6 with mission information but no starship class listed. 

There is some out of universe information that suggests Helin was a lightweight Oberth class ship (notably, a commemorative plaque given to Eleanor Helin, the astronomer who the ship is named after), but this information doesn't appear in-universe and seems contextually at odds with the ship's limited history.

So here's what we know about her. Helin was built some time after 2280, and would have normally operated in a task force with a light cruiser and a frigate as escorts. As a "true carrier" she would be expected to conduct power projection and humanitarian operations and very likely came info conflict with either Klingon or Romulan forces in the early years of her life. In 2293, she was patrolling the neutral zone when Starfleet proposed assembling a fleet of 18 starships at Starbase 24 to penetrate into Klingon space, secure the orbitals of the Beta Penthe system and then support a ground assault on the prison colony at Rura Penthe. The goal was to evacuate James Kirk, Leonard McCoy, and presumably other Federation citizens held at that facility. Helin (under the command of Captain Rebecca Brookshire) and U.S.S. Scovill (NCC-1598, NVS configuration) would have provided shuttle support for the fleet, and would have been essential for moving ground forces and evacuees through the prison's electronic frontier.

Of course, Operation RETRIEVE was never authorized, and Kirk and McCoy ultimately departed Rura Penthe through their own efforts. This was probably for the best, since a major incursion into the interior of the Klingon Empire surely would have prevented the successful conclusion of the Khitomer Accords later that year. 

We don't know Helin's ultimate fate, but like the Chicago class "heavy" cruisers, the NCV type shuttle carriers weren't designed with long-term sustainment in mind. It's likely that her service life came to a close not long after the conclusion of the Khitomer Accords. Even in the fact of the growing threat of the Andromedan crisis in the 2290s, the cost and diminishing returns of operating an NCV would start to become unmanageable.