Tweaking Memory usage for drupal in shared cpanel environment possible?

Yes, when there's no cushion you need to fine tune your sites to save RAM.
Go through the apache and mysql tuning articles, altough tweaking these may need the host's intervention.

In cpanel, KeepAliveTimeout is 15 seconds by default, so get it lowered to 3-5 seconds.
Then turn on and configure Query Cache in mysql, which is also off in cpanel by default.

If you can, try to run the script mentioned in http://drupal.org/node/85768 to see if things like open tables are under control.

Now, php may take 16+ MB RAM, but the whole of an apache process usually grows to 25 MB or more.
On top of that, mysql allocates 1-5 MB more of RAM per connection to handle sorts, joins and reads.
So RAM usage per page can be an issue, but only if the site is highly dynamic like a forum.
For regular sites, cache modules and software can keep traffic under control.

In drupal, see that you don't use unnecessary functionality, like collecting statistics that could be taken by google or the server.
If you have views + cck, the performance techniques do help, cutting page generation time.

Actually, very few hosts that I've looked at limit your storage usage. A few more block your usage of php.ini or settings.php to override memory.

So tell your host that if they don't remove your storage limit, or at least raise it to a more sane level, that you will go elsewhere - and be prepared to do so. You don't need a server of your own for the traffic you're getting (it's low). There are plenty of budget hosts that will let you do what you want.

I would suggest you avoid the hosts that have a separate MySql server (such as Dreamhost) because these tend to be problematic, especially for lower traffic sites (can't keep stuff in cache long enough). There are many recommendations out here on DO.

Nancy W.
Drupal Cookbook (for New Drupallers)
Adding Hidden Design or How To notes in your database

Your concerns are right, but configuring and managing a server is the core of the hosting business.
What happens is that there's a grey zone between the small sites and the large sites where the usage won't fit the price.

Out of this zone the scalability works as normal, where shared hostings are the bottom of the ladder.
VPS is one step up, in which you get isolated resources, but usage must be calculated carefully.
Only the entry level VPS have a price advantage, as entry level dedicated servers cost the same as a large VPS.

At this point, you just have to weight the cost of tuning a system against spending a few dollars in a better hosting.
For example, cpanel license cost monthly fees, which are supposed to lower the cost of managing a server.
Of course, non-commercial sites are bound by the dollars, so tuning must be made.

Back to drupal, limiting the RAM only limits the site to work with less modules.
See if you can benefit from cache, so check drupal cache, mysql query cache and cpanel also comes
with zend php optimizer, which is a php accelerator.

There's many things that can be done and must be done, but the scope spans across several issues.
Usually, drupal is already optimized for regular cms usage, only special cases must be tweaked.
One needs to search why and where a small site is taking too much generation time and resources.
A forum is not really a heavy module by itself, but it all kind of forums are known to grow rapidly.

Beyond this, you'll need to choose between using modules out of the box or working with php to use programming techniques.
This is the case with Views and CCK, where the initial load can be lessened by using the API, etc.
In most cases, using the advanced functions is still better than creating your own custom module.

try static caching http://drupal.org/project/boost