I can add a bit of Muslim perspective. 1st of all kudos to you and your father for being open about being open to look at other theologies for better understanding.
I would like to start off by saying Christianity and Islam can be looking at the same thing but word it differently. For instance I am of the impression what Christians refer to as grace, we Muslims refer to as God's mercy. Our belief that Allah(swt) is especially merciful when you talk the talk and walk the walk. But his mercy also encompasses Every thing all the time. The murderers and killers will receive his justice rather than his mercy on judgement day. But in this world every recieved mercy all the time. When we commit crimes, he doesn't send the angel of death to pull out our soul. When we don't thank him for allowing us to live and for making our lives fruitful, he doesn't strike is down.
There is a saying I've heard from other Muslims and it goes like this " even if we tried to thank Allah(swt) for each one of the breaths he allows us to breath, we will never be able to thank him enough because for the breath we thank him for we are using another breath to thank him for the previous one".
We believe that Allah(swt) has given us a balance to live by. This world and the hereafter. So we don't worship him every second of the day but rather keep a balance of living this life with the limits while worshiping him. We live this life for the body and worship for the soul. We try to feed the soul and the body daily.
I imagine the concept of being in God's grace mean you are filled with the Holy Spirit and you don't do anything bad because you just don't want to.
There is some contrast to this concept in Islamic theology but the quiet the same. The concept unfold in the 3 levels of faith, Islam, imaan and ihsan. Islam is when you have believed, Imaan is when you practice the basic teachings, prayer, zakat, being nice etc. Ihsaan is when you worship your lord as if he was standing in front of you. The higher your level of faith the more deserving of mercy you are. Allah(swt) say, that if some one makes an effort to be close to him, he makes their path easy" he also say, "if you move one step towards him, he moves 10 steps towards you" shortening the distance.
We also recognize in order to hold faith you have to make an effort. The person who is at a high level of faith, usually with worship and committing to the the right actions, he also has to keep working on it so he doesn't lose it. The heart is the gate way to the soul, as the brain is to the body. So keeping one's heart clean and filled with the light of God takes constantl work or staying away from evil and keep working towards good. There is no cruise control setting for faith. Faith will always fluctuate, increase or decrease depending on your how you keep yourself. When ever we commit a sin, there is a lack spot that appears in the heart and the covers a little bit of that light, do enough bad deeds constantly and the hearts light gets covered by the darkness of sins. Which is why when someone does something bad for the 1st time they feel guilty because the soul doesn't like that it's gateway is being covered, the more bad you do the easier it gets because the soul is starting to shrivel and the darkness increases. We have to constantly keep worshipping and repenting in order for the darkness to disappear and the soul to be nourished. Since the source of the soul is Allah(swt), it's nourishment Is worship and the word of God.