Were I near death, or reasonably believed myself near death and no Orthodox priest were available, I would ask a Roman Catholic priest to hear my confession, anoint me and give me the Eucharist. I would not ask any other Christian minister for the same, but I would ask for their prayers.
I have never thought of it in these terms, other than to attach a crucifix to the visor of my car on which is stated: "I am a Catholic. In case of emergency, please contact a Catholic priest". Since arriving at the Maronite Catholic Church, I have pondered how I might alter that message to read: "I am a Catholic. In case of an emergency, please contact (and give the name and cell phone number of my pastor)." I have heard horror stories from those Maronites refused communion because they were not 'real' catholics.
Canon 844 (4) permits those outside the Catholic church to take communion IF they believe in the Catholic doctrines with respect to the Eucharist, IF they ask themselves (can't offer - they have to ask), IF no minister of their own faith is available, and IF there is danger of death or other grave circumstance. It has to be cleared with the archbishop.
We received under 844 (4) after General Convention 2003 in the Episcopal church, because the archbishop had allowed a family in North Georgia far from any "high" parish to receive at the local Catholic church. We had to ask permission from the rector and had a long discussion about our adherence to doctrine. Since the entire Episcopal diocese had fallen into heresy, it fell under the "other grave circumstance".
Actually, Kolo, thank you for stating this. It goes without saying. There are no Orthodox churches where I am, but I watch EWTN Mass at least several times a week. I attended the Mass for the late Pope JPII in a Catholic Church but did not participate in the communion, of course. If I were on a death bed, and no Orthodox priest were available, I would do the same thing as you said you would -- and for the same reasons: confession, sacraments, prayers. But anyone other than a Orthodox/Catholic priest, I would only ask for his/her prayers.
That's because the only authority any bishop/minister may have is through direct succession leading back to an Apostle of our Lord. The Lord gave the Church and the power to bind and loosen only to the Apostles. No Apostolic succession, no Church. Period. There is only One Church, and anything other than Orthodox or Catholic version of it is not a church as far as I am concerned.