Is it permissible for a girl to marry a competent man without her guardian's knowledge if the guardian prevents her from marrying him for reasons other than those sanctioned by Islamic law?

Marriage is not valid without a guardian (wali) according to the majority of jurists. The woman's guardian is her father, then his father no matter how high, then her son and his son no matter how low, then her full brother, then her half-brother (from her father's side), then their sons, then the paternal uncles, then their sons, then the paternal uncles of the father, then the ruler. If the guardian repeatedly rejects a suitable suitor, he becomes an 'adil (one who unjustly prevents marriage) and his guardianship is forfeited, and the right transfers to the next in line among the agnates.

The deemed suitability (kafa'ah) is in religious commitment. The fact that the suitor is a teacher and you are a demonstrator does not mean he is unsuitable, as long as he has good character and religious commitment and is financially capable.

You should reiterate your advice to your father and seek help from someone he respects. If he agrees, then all is well. Otherwise, present the matter to the next in line among your guardians. If they refuse or a dispute arises, then refer the matter to the judge to marry you.

Some guardians prevent their daughters from marrying a suitable suitor out of desire for money or for personal reasons. This is an injustice that necessitates the forfeiture of their guardianship. If the guardian prevents a woman from marrying a suitable suitor, the guardianship transfers to the next of kin. If they refuse, the guardianship transfers to the legitimate ruler (Sharia judge). The woman must weigh the benefits and harms, and referring the matter to the judge is better, as it secures her legitimate right, benefits other women, deters unjust guardians, and upholds the command of the Messenger of Allah (peace be upon him) to marry the suitable suitor.