If Dems actually cared about winning they'd let guns go. This is the single most effective strategy with the lowest political cost and realistically it costs fewer lives than other potential switches.
The upside/downside for just deciding to let the gun control issue sit, and actively promoting that in messaging, is *way* slanted to upside.
The other good option would be to present and campaign on, nation wide, a more conservative Bernie Sanders 2016 style immigration policy.
Anyone who says the best strategy for them is to cut spending should be banned from politics websites for being politically illiterate.
The trouble with shifting right on guns or immigration is that for the time being and for likely a very long time into the future, the Republican party will continue to assert, even with zero supportive evidence, that the Dems are for gun grabbing and open boarders. And their base will eat it up. And that includes folks that if they actually believed the Dems were more conservative on these issues they'd be open for voting Democrat. But the whole culture of the right has enforced an intense social isolation and cult level of insulation to any outside information gaining traction. There is no point in moderating generally on these issues to win them over. And plenty of downside to reducing their own base for the Democrats as they once again abandon their own to appeal to the unpersuadable.