Lesser Reincarnate before a TR

[ilgriffo]

Let's say I'm just hitting lv 20 with a Wizard, so not capped:

(20 Wizard) : I decide to lesser reincarnate +3 into a fighter
(17Wiz/3Fig): I decide to lesser reincarnate +3 into a fighter (is there a timer on LR+3 again?)
(14Wiz/6Fig): I decide to lesser reincarnate +3 into a fighter
(11Wiz/9Fig): I decide to lesser reincarnate +3 into a fighter
(9Wiz/11Fig): I decide to lesser reincarnate +2 into a fighter

Then I TR into a Wizard again and once lv20 again I repeat the above for, let's say, a rogue.

is this reasoning correct?
is there a timer on LR?

ty all

[Visty]

the timer on any reincarnation is 1week

and yes, its possible to get the fighter past life feat that way but it takes 5 weeks to do so