There is no 'saving too fast.'
People who start out by having a goal of retiring young might save 50% of their income or more. If your lifestyle is what you want it to be, fine, I won't suggest a bigger house, better vacation, etc.
Once the usual accounts are funded (The 401(k) and IRA for a $23K total, you won't have much left if your income has $2000-$2500/mo to save.
Take that extra $1000-$7000/yr, and just put it in a brokerage account, a money market for now. Many have done just fine by buying into a broad index, the S&P for instance, regardless of the market. You mention "stock picks." I am in my early 50s, and learned long ago that stock picking is a tough game. Less than 10% of my retirement money is in individual stocks, and over time I lag the S&P by just enough to calculate the cost of my 'having fun picking stocks.'
If you just throw that extra money aside into the money market, you'll have the funds to buy when an opportunity presents itself, either the S&P or other index if you go that way, or individual stocks that meet your criteria.
There are people that manage to invest 100X the money you're talking about for their own savings. Be patient.
You don't mention your marital status. If you plan to marry and have children, college is expensive. You can open a 529 college savings account in your own name and change beneficiaries when the kids arrive. I'm expecting my 15 yr old's college bills to exceed $200K. This is for one child. That will absorb your 'excess reserves' pretty fast.