My opinion is this, either grind them out or use an excavator with a thumb and frost tooth and forget the bucket cat completely. If its speed your looking for use the excavator, if its farmable land afterwards then grind the stumps, its that simple, try both and see which you want to farm later on, especially a garden basically.
I don't mean to rain on your parade here but from what you described your not going to get it done in a week anyhow, you stand a better chance with an excavator than you ever will with a bucket cat but either way its looking slim to none you'll get it done in that amount of time, especially with no prior experience, unless you have virtually no stumps to take out or they are really small, next if your going to grub off 6 acres and pile the stumps up your going to have a pretty big pile and you need to account for clearing a place to pile or shove them as well, you need to clear even more than you think to achieve this.
I don't know who's timber your going through and pile this stuff in but I doubt they'll be happy when your done. I can go into long detail about how do to each way and what it'll take and how much dirt you'll need to move and how many rocks you'll bring up but the fastest way to grub is with an excavator with a frost tooth to trace around the stumps and rip them out and that will disturb the least soil vs using a bucket cat, a stump grinder will disturb even less your only going to grind out the heart of the stump and leave all the topsoil intact and the rocks where they belong, down under the topsoil.
I don't know what you have for equipment now or plan on having but I'd invest in a skid steer and some attachments and work on it as you go and have something descent to farm later on.
Will any system work, yes, the only difference is cost and speed and amount of soil disturbance involved. Unless you take a large excavator and I mean large your probably not going to get it done in a week anyhow. I guess I'd have to say this, in the end does it matter how long it takes, would you rather have dirt to farm or rocks and clay/gravel. You can have a perfect looking garden when your done if you'd like but the best way to go is how your doing it now, by hand and slowly, the more machines you bring in the more rocks and clay you'll farm later on, it just speeds the process up, so you need to determine how fast it needs to be done and how little physical work you want to put in it.
If it were me I'd go buy a skid steer and put over the tire tracks on it and invest in some attachments to go on it and I'd take my time and do a nice job and work at is as I went, that way I'd have something to use to maintain this with later on as well and to use for other tasks, sounds like you need some machine help to cut and haul wood and move trees with and maintain your road to it through the timber but that's just me. Best of luck
