Not fully baked out, but these are my initial thoughts.
Our biggest difficulty in addressing this topic is our tendency to turn it into an anachronism. What I mean by that is this: we can't read our modern understanding about who deacons are and what they do back into texts like 1 Timothy 3. I'll give you an example. We have all seen churches in the Baptist model that employ a deacon board. Granted, we know this model is unbiblical as a church should be led by a plurality of Elders, but nevertheless, this is the most common context we even have for who and what deacons are and do. Consider the following dialogue
PERSON: "Does Scripture allow a woman to serve in that capacity?"
PERSON: "But doesn't the Bible say Phoebe was a deaconess and the verses in 1 Tim 3 point out that women were called to serve in that capacity!"
ME: "You are correct, it does appear Paul mentions women serving as deacons in 1 Tim 3 and in Romans 16 when he refers to Phoebe."
PERSON: "So why do you say that women can't be deacons you hypocrite, chauvinist jerkwad!"
ME: "Because deacons should not be the leadership of a church, but if they are serving in that capacity, then the clear principles from 1 Tim 2 (mentioned just prior to the qualifications of who can actually lead and be employed in serving the church in 1 Tim 3) would apply. Women are not to have authority over men. So if your definition and job description of a deacon is an individual in a position that has authority over men, then No, women are not Scripturally permitted to occupy the office you are describing. The conflict is between what deacons originally were and what we now presume them to be. So, yes, women can serve the church by carrying out any instructions and general service prescribed by the Elders of the church, but no, they cannot be the ones issuing instructions."
A woman's primary service and focus should be on her own household which is why it makes no mention of her being a one-husband woman and specifically states that the men must be one-woman men. So this would make your pool reduced to single women with the spiritual gift of celibacy who are committed to a life of chastity or an older widow who no longer has a husband to serve due to his death or children to serve due to them being adults.
We do a disservice to the office of deacon both by elevating it to a place of leadership it was never intended and by reducing it to a cute way for people to serve the church by giving them an official title. This is why it is Biblically both non-authoritative and yet so highly restrictive. Not just anyone can be a deacon, they are vetted as seriously as Elders, not because they rule the church as Elders do, but because they are committed to serve the church extensively. They are more akin to church staff than mobilized lay people in some regards. You vet your church staff more exhaustively than you do your bass player in the band, while understanding both require some level of examination. But Elders are examined and tested most stringently because they occupy the highest role of the church, leading it, shepherding it, teaching it, protecting it, serving it, etc… Deacons help the Elders serve the church by doing what the Elders need them to do, not a separate authoritative body operating independently.