Was this a total donk 3 bet cold call?

1-2 with a 5 dollar bring in straddled to 10. One EP limps MP opens to 45 , another MP calls, CO pots to 180(who I perceive as likely 3 betting fairly wide,) super loose SB calls. I have 6677 single suited. I'm 1200 effective with SB, but 500 effectiveish with most of the rest of the hand. I decide to cold call thinking that I will bring along at least the opener and the cold caller, and maybe others.

I can either flop a set, a straight, or a straight and a flush draw and get it in, or easily fold out on flop.

At least that was my thought process, but the straddle then jams 500, the limper, opener, and field caller fold out, 3 better jams for a bit over 500, and SB jams for 1200. My immediate reads is that the straddle and 3 better probably have pretty solid, higher card hands, and the SB can pretty much have any 4, and be trying to deny my equity. I end up making the call thinking I'm likely doing pretty well if at least 2 of the villains are sharing high cards with each other.

3 better ends up having pretty decent kings, straddle had a high card rundown, and sb had JJ 5 2 rainbow. I end up getting scooped, but when I ran the equities, and equities with similar holdings of my opponents perceived ranges it appeared that I was actually getting fairly good equity usually.

Regardless, I still feel like the cold call put me in a very precarious position, that I didn't necessarily need to be involved in.

Was this a big punt? I've relatively recently gotten into 4 card as a Hold'em player, and while I know that middling double paired connected cards with a suit are quite a strong holding, I'm not sure if it was strong enough to justify the cold call in the SB. I'm used to just never cold calling 3 bets in Hold'em, so the concept that it is sometimes a viable strategy in 4 card is a difficult concept for me to grasp.

Thanks in advance for any replies.