With the understanding that the desired term has already been found in "heuristic", I'll still venture another H-word for the Googlers out there :)
Honest effort - an effort which is "in good faith" or "showing fairness and sincerity; straightforward; free from deceit." However, while I cannot find any official definition of this, I feel in common usage it has a more complex meaning.
That meaning that I understand for it, is as an unsophisticated good-faith attempt which falls shy of perfection.
"while this first cake is an honest effort, the second cake wins the prize." - this doesn't imply that the first cake is a bad cake, it doesn't say it's a failure, it's just not a best-in-show cake. It's still a tasty, good-looking cake, though.
Quotes I've found include:
It was an honest effort, but the team ended up apologizing, sort of. [Wizards apologize if Black History Month tribute 'missed the mark']
-- Washington Post, Feb 3 2016
It was an honest effort, but a mistake nevertheless. His attempt to handle Rosecrans with gentleness backfired.
-- Halleck: Lincoln's Chief of Staff by Stephen E Ambrose, 1996
The exempt counties are reliably Republican outposts, so currying favour with constituents is a likelier explanation than outright racial animus. “It was an honest effort to recognise that across the state there are variations in the ability to get jobs.[...]"
-- The Economist, May 17 2018
His first mixtape, "The Purple Tape," surfaced in 2012, when he was 18. Looking back, he realizes its limitations. "I thought I was ready, but it was really immature," he says. "I was talking about cool stuff other teenagers were doing. It was very vain. It was an honest effort, and true to everything I was doing at 17, 18. But it's definitely night and day between then and now." -- Joey Purp, Chicago Tribune Aug 8 2018
We were begged not to punish the State of Idaho for a mistake, if it was a mistake, in regard to its own organization; for it is said they made an “honest effort” to comply with the law
-- Congressional Record, 1892
This usage seems to fit both with the "not optimal" current phrasing, and with the "not sophisticated" previous phrasing of this question, tough of course the meaning is far removed and more negative from that of heuristic.
Heuristic typically implies "industry standard rule of thumb"-type competence.
An honest effort instead implies "giving it your best shot and getting close", often with implications of failure-through-inexperience.