Should I have my Luxman R-115 repaired?

Luxman should not struggle with driving 105/3 if you properly service your receiver. Make sure you prepare your receiver by overhauling it completely. At least what should be done is replacement of main filter power supply caps, but if you know you have distortion, than you might want to step into complete rebuild of BOTH channels. Bare in mind I usually replace caps with larger capacitance. Today there's better availability to replace originals with larger value for larger current reserve thus giving new possibilities of receiver to drive heavier loads.

When I service, I inspect signal path of amp and preamp with speakers or headphones with loose unterminated  leads to define a proper "menu" of restoration.

In poweramp section I usually check for bad solder joints and if they are around power transistors, I'd replace all power transistors(fortunately power transistors are cheaper than power tubes:)). Another sign of necessary replacement of power transistors is dry heatsink compound. If you have one or both channels distorted, it's mostly in driving on preamp stages. 

I'm local to North Carolina Raleigh-Durham and I do not ship. My flat rate for your reference (if you're shopping for repair techs) is $160+ parts. Parts may run anywhere from $20 to $150 depending on availability and pricing. 
Be noted that sometimes I have to wait for parts few weeks before getting them even if ordered from highly reputable sites such as Mouser or Digikey.

I may be shopping for a tech but I'm at the very western tip of North Carolina, a long way from Raleigh.  I'm located 2 hours north of Atlanta; 2 hours west of Asheville; and 2 hours east of Chattanooga.  Or, as many say, 2 hours from anywhere.

i agree with willand, as i usually do--it's not worth fixing if it costs more than $150 or so. the real luxman collectibles are the earlier "suckface" models (rx101, rx102, etc.), which don't necessarily sound better, but are more sought-after and valuable.

Indeed you live in very nice far-aways, but would probably advise you to shop for tech in Chatanooga, Nashville or Atlanta.
From the stand point of person directly dealing with vintage audio sales and services, believe me it's well worth $150+parts to overhaul your receiver.
Fully overhauled unit sells near $500 and capable driving heavy speakers.
Moreover, you won't loose a dime when you will want to upgrade after "time passes". By simply dumping it you will certainly loose more. At least these units can be sold as-is for service or repair and still have value. 
Another option to try is getting Crown XLS1000 pro-audio 2ch amp for low $200's that has xlr and RCA unswitchable inputs and volume control for basically all your needs for the time being.