A further six starts have followed in the league, with four more appearances off the bench, and altogether he has notched up 16 appearances - a vast improvement on last term.
His last RaboDirectPRO12 game saw him line up against former employers the Blues, and while on the losing side 21-13, the 21-year-old knows it's all about the long game as he looks to prove his worth.
"It's been unbelievable for me this season. If you had told me last year that I would have made this many starts already I would have bitten your hand off," said Screech. "It's been really good for me to be around the team.
"I had another year on my contract with the Blues but they released me early. I went to Bedwas with the agreement to train with the Dragons.
"My ambition was just to come in and try and impress through the year but obviously it got brought forward quite a lot.
"But it is nice to know I have the security of a three-year deal, it means I can concentrate on what I need to do and keep my head down.
"I was really looking forward to the game against the Blues and trying to make an impression and almost prove to them that they should not have released me.
"I was quite pleased with my performance, it is all about the learning curve for me at the minute and I would like to think that next time I will be even better."
Having represented Wales at Under-16 and Under-18 level, Screech formed a key component of the Wales Under-20 team that created history in 2012 by becoming the first side to beat New Zealand at the Junior World Championships.
And while it did not propel him to further success at Blues, his potential was picked up by director of rugby Jones.
He has already encouraged his player to follow the example set by Wales and British & Irish Lions lock Alun Wyn Jones, and Screech knows he owes a debt of gratitude to his current mentor.
"Lyn is the one who thought I had something and the one who offered me a contract," he added.
"He has really helped me to bring on my game and I'm looking forward to working with him more.
"It's a big comparison hearing him talk about following in the footsteps of Alun Wyn Jones. Hopefully I can live up to the reputation and do some of the things he has done in the next few years."
In the short term, Screech is looking for his Dragons side to maintain their winning momentum, particularly for when the RaboDirect PRO12 resumes next month after European and LV=Cup duties.
"We want to win as much as we can. We are sixth in the league but it is quite tight between the people below us," continued Screech.
"We want to make sure we stay on top of that little group of teams in the middle. The next target is fifth and moving up.
"I think we are playing really well at the minute, we have improved a lot since last season. We've won some big games like against Ulster although there is still room to get better."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up to our newsletter for regular updates on the RaboDirect PRO12
63x46.png){kind=logo}