Your Question:

I really like the heavy tannins/earthiness of the Nebbiolo and Negroamaro wines.  However, almost all of my experience with these wines is at a very high price point (i.e. from Altamura).  Are there any good-tasting Nebbiolo or Negroamaro wines at moderate price points?

Great question! This may be a long answer, but I hope it provides clarity. First I explain why Nebbiolo is so expensive, second I provide some examples of affordable versions, finally I talk about Negroamaro and how to find affordable alternatives to that as well.

The Altamura brand in particular is quite expensive – partially due to the brand name, but also due to the land and aging. Try looking at other regions, like Italy (where these wines originated!) and you’ll have much better luck finding all sorts of price ranges (they will also range in quality, but you get a lot more bang for your buck!). 

Barolo and Barbaresco are regions in Italy and the name of the wines grown in their towns. Not to be confused with Barbera which is a grape varietal (I remember it by the “O’s” BarolO, BarbarescO and NebbiolO all go together. BarberA is A grape). 
Barolo is the King (stronger, more powerful profile) and Barbaresco the Queen (more floral and delicate profile) of Italian wines. They are 100% Nebbiolo wines and have the strictest growing and aging requirements of all regions that grow Nebbiolo. These wines are expensive because they cost so much to make. 

Did you know that Barolo requires 3 years of the aging total with a minimum of 18 months in oak? That’s just the basic level, riserva must be aged for a minimum of five years total! For Barbaresco the aging minimum is two years total with nine months in oak, Riserva wines must be aged for 4 years total. That’s a long time to wait for a paycheck! Not to mention the storage and the fact that oak is not cheap. So that’s why you find that most Nebbiolo wines are so expensive. 
This is true of many various types of aged wine. If you like this style but want more affordable – look at Spain. It’s grossly underrated and you can buy a Gran Riserva (aged the longest) Rioja (Tempranillo-based wines) for about $30. These wines will be aged similar lengths and similar ways, although Spain more often uses American oak instead of French.  
Here are some more affordable Nebbiolo options I recommend:

• Castello di Verduno Barbaresco, I have not personally had this wine, but I hear it’s excellent and comes very highly recommended by distributors I trust. This one is $45. 
• G.D. Vajra has incredible value Italian Nebbiolos at various price ranges: Nebbiolo Langhe (the same overarching region where Barolo and Barbaresco are, but not exactly within those town limits, so it must be called Nebbiolo Langhe instead). This is about $25 and a GREAT value wine! I love pretty much everything G.D. Vajra produces. 
• Renato Ratti is also very good and can be found at France44. That will run you about $55. 
• 2017 Villa Guelpa Sizzano Piedmont is another I have not tried but has gotten rave reviews, and it’s under $40!
• For American styles, look at Barboursville Nebbiolo from Virginia. It’s first-rate and will cost about $36-$40 depending on where you get it. Virginian Nebbiolos are really coming on the market as it’s recently been discovered that the climate is well suited for that specific varietal. Get them at affordable prices while you can!

Negroamaro is a little different – there are many, many, many, affordable versions of this grape, that you could be hard-pressed to tell the difference from Altamura if blind-tasting, that are a fraction of the price. 

Salento and Puglia are the most common regions you’ll see – they have great value wines starting at $22! 
Also, look for Terra d’Otrano DOC which is another great region with Negroamaro based wines (included rosés!). 

Here’s Tomaresca Negroamaro Salentia Masseria Maime for $35. You’ll also see many Negroamaro and Primitivo wines from Italy for a blend – the Primitivo (Zinfandel) helps to round some of the rustic traits of Negroamaro. 

I hope this helps! Let me know if you have any further questions.