We will first introduce the stringency of “right before Shabbat” that you refer to and then apply it to your case.
There are two categories regarding having foods on a flame on Shabbat (irrespective of the melacha of actually cooking on Shabbat): shehiya and chazara.[1]
Shehiya means leaving a pot/food on a flame, after putting it there to cook or to heat up before Shabbat. In certain situations, it is permitted to leave the food on any heat source; in others (the subject of a machloket since Talmudic times[2]), something must be done to reduce the chance that one will “stoke the coals” or its equivalent. The bottom line is that blechs[3] and nonadjustable hot plates[4] fulfill the halachic requirement, when necessary.
Chazara refers to returning a food to a heat source, classically on Shabbat, after it had been removed previously. Chazara has more stringent requirements than shehiya (for reasons that exceed our present scope). In order for it to be permissible in the classic case (i.e., on Shabbat), five basic requirements must be met: 1) The food is fully cooked; 2) the flame is covered;[5] 3) the pot remained in one’s hand since being removed; 4) the remover had in mind to return it to a heat source; 5) the food is still somewhat warm when returned. Only condition #2 applies to shehiya.[6]
The general assumption – that the core difference between shehiya and chazara is that the former applies when the food is left on a flame from before Shabbat and the latter applies when one puts food on the flame on Shabbat – is challenged by the following gemara:[7] “According to the one who says that people may do chazara, this is true even on Shabbat.” This implies that there is a case of chazara that is not on Shabbat (and that it is less problematic to permit than chazara on Shabbat). Tosafot[8] explain that this refers to putting the food back on the flame so close to Shabbat that if the food were cold, it would not have a chance to become hot before Shabbat. Although several Rishonim disagree with Tosafot, the Rama[9] says that it is proper to follow Tosafot’s opinion.
If putting food on the flame at that time is indeed chazara, does this mean that most or all of the aforementioned five conditions of chazara must be satisfied, a possibility your question seems to entertain? Actually, it does not. The five conditions of classic chazara can be broken up into a few groups, based on the problems that they solve. One concern is that putting the food on the flame should not result in violating bishul[10] on Shabbat. This is taken care of by conditions #1 (already cooked) and #5 (still warm, which is a requirement for liquids[11]). However, one cannot violate bishul by putting food on a heat source before Shabbat, and we have no source for a Rabbinic extension to Erev Shabbat.
So in what way is chazara close to Shabbat worse than shehiya? It applies at least to condition #2 (a covered flame), making it a requirement in more cases than it is for shehiya.[12] There is an opinion[13] that conditions #3 (food in hand) and #4 (intention to return), which are special stringencies of chazara, are in effect also right before Shabbat. However, the accepted opinion is that the stringency of “right before Shabbat” applies only to condition #2.[14] Since a nonadjustable hot plate is no worse than a blech (which solves #2), you do not have a problem.