Scott is probably going to give you some good insight here, but I'll take a stab and maybe save him some time in typing. Or get a conversation going at least 
So a few things really stand out to me personally reading your post. So I have a few questions, and take this as helpful questions/comments and in no way criticism.
After 3 weeks do you feel like if you went to the gym you'd be unable to hit PRs? Are you looking at any other symptoms of over reaching beyond a desire to take a rest? Sleep disruption or loss of appetite, etc? In addition, how bad are your joints hurting after 3 weeks? Has this always been common? To me personally this seems like if your joints are hurting after 3 weeks, it's pretty soon. There could be an issue with the lifts you are choosing, and they do not work biomechanically for you. Or possibly, the method in which you are lifting may be too ballistic or loose in nature, and would benefit from some form adjusting.
Do you have any additional indications about this "subconsciously lost desire to train, or do things only for fun" besides a hunch? This I'm not sure anyone can help you with besides your own internal gut check. From your post it seems like you are really training damn hard. But might be a personal question you need to really ask yourself. As well as what your goals are. If you are getting out of training what you want, then what you are putting in may be wholly and completely appropriate.
As far as food goes, hard to tell without knowing exactly what your food is between day to day. Is the gap big? small? Do you feel like you are really hungry on off days? Do you feel like you are more or less recovering between days. I know I am personally experimenting with a reverse diet where I am adding in food only around training right now, and at times it for sure is a challenge, but I can say soundly, that maybe 12 hours after training I feel VERY hungry, and not so fresh, but 36 hours later I'm feeling much more sated and better.
All of this being said, given that recovery is on a personal and on a sliding scale. Cruising at 3 weeks may be just what you need. I also know a host of people who train one on, one off for FT and found that really helps. So a day off in between every training day, instead of two days being back to back has helped them sustain a blast longer and feels more productive.
For myself, since you mentioned. I typically cruise after 4 weeks, but mostly that has to do with lifts either stalling, or regressing slightly, or I can feel my intensity and training desire start to dip. Rarely is it due to joint issues or injury. I have in the past pushed to 5 and even 6 week blasts, but always felt those last week or two were not completely, but somewhat unproductive at the gym. Also, that the longer cruises left me feeling slow to start. I may cruise a bit sooner that most people would prefer. I just personally found it better to bow out of a blast with my training at a 7 or 8 out of 10. And then roll into a cruise week hitting 9's and start my next blast at a 10. Then go longer and have my training sitting at a 5, through my cruise it being 6's and 7's and starting my the first half of the first week of my blast at 8's and only really getting into a good groove until after that.
Anyway, Lots of rambling here, which I tend to do. Hope some of this helps or gets you in the right direction. Interested in hearing back and of course what the Doctor himself has to say.
So a few things really stand out to me personally reading your post. So I have a few questions, and take this as helpful questions/comments and in no way criticism.
After 3 weeks do you feel like if you went to the gym you'd be unable to hit PRs? Are you looking at any other symptoms of over reaching beyond a desire to take a rest? Sleep disruption or loss of appetite, etc? In addition, how bad are your joints hurting after 3 weeks? Has this always been common? To me personally this seems like if your joints are hurting after 3 weeks, it's pretty soon. There could be an issue with the lifts you are choosing, and they do not work biomechanically for you. Or possibly, the method in which you are lifting may be too ballistic or loose in nature, and would benefit from some form adjusting.
Do you have any additional indications about this "subconsciously lost desire to train, or do things only for fun" besides a hunch? This I'm not sure anyone can help you with besides your own internal gut check. From your post it seems like you are really training damn hard. But might be a personal question you need to really ask yourself. As well as what your goals are. If you are getting out of training what you want, then what you are putting in may be wholly and completely appropriate.
As far as food goes, hard to tell without knowing exactly what your food is between day to day. Is the gap big? small? Do you feel like you are really hungry on off days? Do you feel like you are more or less recovering between days. I know I am personally experimenting with a reverse diet where I am adding in food only around training right now, and at times it for sure is a challenge, but I can say soundly, that maybe 12 hours after training I feel VERY hungry, and not so fresh, but 36 hours later I'm feeling much more sated and better.
All of this being said, given that recovery is on a personal and on a sliding scale. Cruising at 3 weeks may be just what you need. I also know a host of people who train one on, one off for FT and found that really helps. So a day off in between every training day, instead of two days being back to back has helped them sustain a blast longer and feels more productive.
For myself, since you mentioned. I typically cruise after 4 weeks, but mostly that has to do with lifts either stalling, or regressing slightly, or I can feel my intensity and training desire start to dip. Rarely is it due to joint issues or injury. I have in the past pushed to 5 and even 6 week blasts, but always felt those last week or two were not completely, but somewhat unproductive at the gym. Also, that the longer cruises left me feeling slow to start. I may cruise a bit sooner that most people would prefer. I just personally found it better to bow out of a blast with my training at a 7 or 8 out of 10. And then roll into a cruise week hitting 9's and start my next blast at a 10. Then go longer and have my training sitting at a 5, through my cruise it being 6's and 7's and starting my the first half of the first week of my blast at 8's and only really getting into a good groove until after that.
Anyway, Lots of rambling here, which I tend to do. Hope some of this helps or gets you in the right direction.
Interested in hearing back and of course what the Doctor himself has to say.