I do not find that the Greek often solves these difficulties. However, because of your request we will look there first. The Greek word in Titus 2:5 translated "keepers at home" is (in its anglicized form) "oikourous." According to Thayer's Lexicon, it refers to the keeper or watcher of a house; to one who keeps at home and takes care of household affairs. According to Vine's Expository Dictionary, it refers to those who watch or keep the home. Strong's Concordance states, "a stayer at home, i.e. domestically inclined (a 'good housekeeper')." The Greek word is a compound word made up of oikos, meaning an inhabited house or a home, and ouros, meaning one who keeps or watches over something; hence, the meaning "keepers at home." The word, oikos, is quite common in the New Testament. The word, ouros, is found only in compound words like kepouros which means keeper of the garden or gardener.
I normally do not go into all the Greek background but I did so here for a couple of reasons. First, it is unnecessary. You do not really know any more now than you did with the English. The Greek is fairly general in meaning and that is why the English seems so. The phrase in Titus 2:5 refers to one who keeps the home; that is, cleans the floors, cooks the meals, makes sure the needs of the home and its inhabitants are cared for. That is clear from the English and is no more clear because of our study of the Greek. Second, I wanted to point out the danger of selective choice in interpretation. To take the single Strong's mention of "stayer" and make a doctrine out of it is dangerous. (I know you also mentioned English dictionaries and I will get to them later.) But even in Strong's, stayer is not a reference to someone who cannot leave the home. He explains his meaning with the "i.e." It refers to a "good housekeeper." I often see people wanting badly to prove something, so they go through the reference books until they find one word that seems to support their belief. Then, they hold to that word and teach their approach as absolute fact. I am not accusing you personally, but only warning of this danger.
So, what about the English phrase? What is a keeper at home? I am not sure what you mean by older dictionaries. Webster's 1828 has many definitions for keep, but I could not find where the word, stay, was used in conjunction with keep. In reference to the phrase, to keep house, Webster gives two definitions. The second is to "remain in the house; to be confined." Here is the example he gives for this definition: "His feeble health obliges him to keep house." This definition is also given in the Oxford English Dictionary, but we can rest assured that "keepers at home" does not refer to confinement to a house because of sickness. This is straining at a gnat to swallow a camel.
Our best approach is to return to the normal meanings of the words. A keeper is one who has charge, care, or oversight over something. A wife is to have charge, care, and oversight of the home. That is the place of her dominion and rule. The first biblical reference to "keep" is in Genesis 2:15 where God takes man and puts him "into the garden of Eden to dress it and to keep it." Adam was responsible for the care of the garden. A wife is responsible for the care of the home. She is the housekeeper and homemaker. Or, perhaps we should call her the homekeeper.
One final note: I am very much for ladies not taking outside jobs so they can stay at home with their children. My wife did so and we are thankful she did. Many would read the injunction for wives to be keepers at home and conclude that they cannot do that and also work outside the home. That was our conviction for our home and I certainly support those who come to the same conclusion. However, others do not come to this conclusion and I will not change scripture or stretch it in order to make my personal conviction binding on others. Neither will I accuse them of disobedience when the Bible does not specifically call it that. God works with people at different places in their lives. Sometimes we need to let Him do His work. I think it is much better for a wife to quit her job because God has dealt with her about it for the sake of her home than because she is threatened by the judgment of God--a judgment that is not specifically taught in scripture. I have seen women at home who harmed their children because of their ungodly attitude and I have seen women who had to work bestow such love on their children when away from the job that the children were truly blessed. When it comes to God's personal dealings in our lives, one size does not fit all. May the Lord bless you in your service to Him.