I am 26 years old and although I got my upanayanam done when I was 13, I never took professional education studying the Vedas. I am interested in learning to chant them starting from the scratch. I understand that it normally takes 18 years of full time schooling in the patashalas to complete professional vedic study. But do they generally admit working men willing to devote only a few hours for vedic study every day into the patashala? And if so, how does the learning process generally go? If I am a Yajur vedi from a certain sampradaya, does that mean I get to learn only the Yajur samhitas? Or do they teach more?
It is very nice to know that you have developed interest in Vedic studies so I congratulate you for that. As less people are now interested in this field.
You have already got the sacred which is a good thing. Now you can commence your Vedic studies there is no harm in it. Before that you can do some prAyashchita (if you have not done gAyatri and sandhya etc.) and start doing sandhyA vandana along with gAyatri again.
Secondly, in the pAthshAlAs, they teach you mainly the samhitA portion of the Veda. In your case it will be Shukla yajurveda samhitA. (Because you sound like a north Indian). Yajurveda has two classifications viz. Shukla and Krishna yajurveda. Shukla yajurveda is mostly followed in north and its samhitA is called "vAjasneyi samhita" and KY is followed more in south and its samhita is "taittiriya samhita".
Usually, the dwija has to first learn his own Veda shakha (Shukla yajurveda/ mAdhyandina shakha in your case most probably). After studying your veda if interested you can study other vedas as well. But first you should learn your own veda else you may incur shAkhAranda dosha.
As the yajurveda has about 1800 mantras, it usually does not take a very long time to learn it unlike the Rigveda which has 10000 plus mantras. So do not worry that the studies would take 18 years.
The basic learning of veda is the samhita. That is learning to chant the samhita with the right swaras. However, there are multiple levels of chanting the veda samhita for the advanced student. These have repetitions of syllables and chanting in forward or backward manner.
The various pathas or recitation styles are designed to allow the complete and perfect memorization of the text and its pronunciation, including the Vedic pitch accent. Eleven such ways of reciting the Vedas were designed - Samhita, Pada, Krama, Jata, Maalaa, Sikha, Rekha, Dhwaja, Danda, Rathaa, Ghana, of which Ghana is usually considered the most difficult.
The students are first taught to memorize the Vedas using simpler methods like continuous recitation (samhita patha), word by word recitation (pada patha) in which compounds (sandhi) are dissolved and krama patha (words are arranged in the pattern of ab bc cd ...); before teaching them the eight complex recitation styles.
A pathin is a scholar who has mastered the pathas. Thus, a ghanapaathin has learnt the chanting of the scripture up to the advanced stage of ghana. The Ghanapatha or the "Bell" mode of chanting is so called because the words are repeated back and forth in a bell shape. The sonority natural to Vedic chanting is enhanced in Ghana. In Jatapatha, the words are braided together, so to speak, and recited back and forth.
The samhita, pada and krama pathas can be described as the natural recitation styles or prakrutipathas. The remaining 8 modes of chanting are classified as complex recitation styles or Vikrutipathas as they involve reversing of the word order. The backward chanting of words does not alter the meanings in the Vedic (Sanskrit) language. Wiki
So basic vedic chanting wont take you so many years. If you are sincere then you can learn in 2-3 years. Then if you wish you can learn the advanced chanting and go up to the ghana patha which is the last chanting level. After completing ghana the vedapathi is considered to be an expert in this area.
If you are not having enough time to enroll in full time vedic studies then you can also learn it part time. Some people learn it during weekends. This option is also available. Instead of going to a pAthashAlA you can also learn from a tutor who is a good veda pathi himself. So personal/individual coaching is also another way.
Now if you are wondering where to find the veda pAthis and gurukul then you may have a look at this list and approach the nearby gurukul or veda pathis.