Consider not having healing
D&D is a game of choices, you always have to carefully weigh up the cost of choices.
Spending a feat uses up a valuable ASI. Choosing a multiclass uses an entire level. Even spending 50 gold is 50 gold you can't spend on something else, plus it takes up room in your backpack and weight on your back.
We often feel that we absolutely need a healer and healing, but "we need healing" isn't a problem, that's actually a solution. Your problem is that you want to fight more, win more fights, or more loosely, achieve more. Is this the best use of your resources in order to handle your problem?
Instead of spending significant resources to get a small amount of healing, consider if it is instead better to maximize your advantages.
A party is taking some damage in fights. A glass cannon wizard is considering multiclassing as a cleric to gain some healing options. Instead, they could get another level of wizard allowing them to deal more damage, expend more spell slots, and even pick up a control spell, that would allow them to kill enemies faster and reduce the amount of damage the party takes.
It is likely that any other choice will be more effective than options that being a level 1 cleric offers.
Generally speaking I think that levels, feats, and items magnify the effectiveness of a character, so making choices that work well with the character will be far more effective than trying to split your role.
Healing isn't all that powerful in 5e in the first place. A 4th level life cleric's channel divinity heals 20 hp (between 1 and 2 attacks from a CR 4 creature), their prayer of healing is 4 + 2d8 + modifier (again, between 1 and 2 attacks which they can do 3 times), cure wounds is 4 + 1d8 + modifier (between half an attack and 1 attack, 4 times). Even a 4th level cleric is not super useful - and I doubt anyone would want to completely reroll. There are better ways to use your resources.
So what alternatives exist?
Now, there are some obvious options: deal more damage to kill enemies faster so they can't hurt you, use control spells to prevent enemies from dealing damage, etc. However, fights are not so 1-dimensional.
Talk instead of fighting
A fight avoided is a fight won. If you have a character that is good at social interactions, then they should work to maximize that effect. Other characters can even help them with spells or feats. Remember that if you skip a fight, then you have a whole fight's worth of resources (spell slots, per-rest features, and HP) that you can afford to spend on the social interaction instead.
Make sure fights are favorable
Better scouting and positioning can be hugely beneficial. There is a big difference between attacking an orc raiding party when they are on the war path, and attacking them while they are cooking dinner and getting ready for bed. Try to maximize your party's ability to take fights on their own terms rather than using HP to account for unfavorable conditions.
Use your time more efficiently
Consider the value of rests. Often we think of rests as being something we can't control - no matter the party composition you get X short rests and 1 long rest per 24 hours and you have to get the same amount of work done no matter what, but that isn't true. Your party controls what it does, that means they could take a lot of short rests, and take less fights per day to make up for the lack of healing. This means you have a lot more down time which can be spent for downtime activities, waiting for the rogue to scout, and social interactions. If your party already has ways to capitalize on downtime, consider taking more short rests per days and taking less combat per 24/hours.
While there are few ways to solve the problem of "we need more healing", there are tons of ways to solve the problem of "we want to accomplish more".