I also wanted to mention that whatever you might suggest must be dog-friendly as I have two small dogs that use the space daily and have a penchant for eating things they shouldn't!

Asiatic garden beetles can be tricky to manage, especially because the adults are highly mobile and can fly long distances in search of host plants. 

At this time of year, late fall, I would recommend waiting on applying any of the control tactics I will detail below. This is because at this time of year these control tactics will not be effective due to multiple factors like climate as well as because of the beetle/grubs' life stage. At this time of year the immature beetles (grubs) will be burrowing deeper and deeper into the soil, where they will spend the winter months. At this time, you may support predation of grubs by tolerating any animals like crows and skunks and their digging in your landscape to reach the grubs. Adults typically begin to emerge from the soil around the beginning of June.

Some years are more favorable than others in terms of supporting higher Asiatic and other chafer beetle populations. Thus you may find lower populations some years, and higher populations other years. 

Some of your main options for managing the Asiatic garden beetles include trapping, exclusionary netting, entomopathogenic nematodes, Bacillus thuringiensis (Bt), and/or pesticides. 

• Trapping: As you likely know, with your management of handpicking these beetles off plants at night, Asiatic garden beetles are nocturnal, feeding at night and hiding during the day. To utilize this fact, some people have found setting up a light (at a height of about 1 foot) with a pan of soapy water underneath works as an effective trap for reducing adults when their numbers are high. It is best to set this up right when you see signs of the beetles and/or their damage next spring. It is important to note that this management tactic may capture non-target beneficial nocturnal insects, and thus should be used during peak Asiatic beetle population periods as a temporary management tactic. The light trap could also attract more beetles to the area- something to key an eye on and consider when it comes to trap placement.
• Exclusionary Netting: If you have plants that are not well established and may be more vulnerable to Asiatic beetle damage, you could consider exclusionary netting, especially before/during periods of high beetle populations (being mindful that netting would also block pollinators). Netting can be tricky as you would want to ensure you do not trap any beetles under the net with the plant(s); thus monitoring and maintaining the netting is key. You also would want to key an eye on the netting to ensure other non-target animals don't get stuck or trapped by accident. Effective netting is properly secured on all ends to exclude the pest beetles from getting to the plant and its leaves.
• Entomopathogenic Nematodes (EPNs): EPNs are insect killing roundworms that naturally occur in our environment but can be purchased and applied in certain areas as a pest management tactic. EPNs seek out and enter host bodies where they will infect the host with a bacteria; eventually killing the host. The two main species of entomopathogenic nematodes recommended for targeting Asiatic beetles include, Heterorhabditis bacteriophora and Steinernema feltiae, and are best applied to the soil starting in late July/early August through September. Always read the storage and application directions when purchasing EPNs. Most EPNs need to be kept in the fridge until you apply them. 
• Bacillus thuringiensis (Bt): Bt is a soil bacterium that produces insecticidal toxins and is naturally found in nature. In order to work as a biological insecticide, Bt or its spores or crystal toxins must be eaten by the insect. Inside the insect, the crystal toxins bind to cells of the gut wall, and cause these cells to break apart, eventually killing the insect. There are certain strains/varieties of Bt that target certain insects and are available for purchase and application in a home landscape setting. The recommended strain to target most grub species is Bacillus thuringiensis galleriae (Btg), usually sold under the commercial name GrubGONE. The general recommended application window is July through August, but be sure to read the product label and directions for application timing. There are varied results, in terms of Bt effectively controlling chafers. Some have found formulations of Bt that are meant for foliar applications are more effective than granular soil applications.
• Pesticides: A pesticide control choice that is relatively safe to apply and provides excellent control is Acelepryn (active ingredient Chlorantraniliprole) which is found in GrubEx (active ingredients can change periodically so check the product label). This insecticide has low toxicity to vertebrates and has shown no adverse effects on beneficial insects. Acelepryn has a broad application window (May – September; always check the chemical label for the recommended application date window). There are also pesticide options, some of which can only be legally applied by a certified pest control applicator (such as any products with the active ingredient Imidacloprid). Always read the entire chemical label before purchasing and before use, following all directions and using all recommended personal protective equipment (like protective clothing and gloves). Always read the chemical label to ensure the product is labeled for your intended pest, such as grubs in turf. If you choose to use a pesticide I would recommend only treating areas of your lawn that have been affected by grub damage, this reduces the amount of pesticides you would need to use. It is important to note that with any pesticides there could be negative non-target impacts on wildlife like pollinators. Pesticides should be carefully considered before purchasing or applying. Not all pesticides are the same, some are more toxic than others.